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|00000000| 54 55 54 4f 52 20 30 36 | c7 4a 00 00 8d 04 00 00 |TUTOR 06|.J......|
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|00000020| 69 6e 63 65 20 74 68 65 | 20 70 61 72 61 62 6f 6c |ince the| parabol|
|00000030| 61 20 68 61 73 20 61 20 | 76 65 72 74 65 78 20 61 |a has a |vertex a|
|00000040| 74 20 28 11 33 68 11 31 | 2c 20 11 33 6b 11 31 29 |t (.3h.1|, .3k.1)|
|00000050| 20 3d 20 28 2d 33 2c 20 | 33 29 2c 20 74 68 65 20 | = (-3, |3), the |
|00000060| 65 71 75 61 74 69 6f 6e | 20 0d 0a 00 6d 75 73 74 |equation| ...must|
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|00000080| 69 6e 67 20 66 6f 72 6d | 2e 12 38 0d 0a 00 20 20 |ing form|..8...  |
|00000090| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000000a0| 20 20 11 33 68 20 20 20 | 20 20 20 6b 0d 0a 00 20 |  .3h   |   k... |
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|000000c0| 20 20 20 11 34 21 20 20 | 20 20 20 20 21 0d 0b 00 |   .4!  |    !...|
|000000d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
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|00000100| 20 20 20 20 20 20 20 20 | 20 20 11 32 32 0d 0b 00 |        |  .22...|
|00000110| 20 20 20 20 20 11 33 66 | 11 31 28 11 33 78 11 31 |     .3f|.1(.3x.1|
|00000120| 29 20 3d 20 11 33 61 11 | 31 28 11 33 78 20 11 31 |) = .3a.|1(.3x .1|
|00000130| 2d 20 28 2d 33 29 29 20 | 20 2b 20 33 20 20 20 20 |- (-3)) | + 3    |
|00000140| 20 20 20 20 20 20 11 32 | 12 31 53 74 61 6e 64 61 |      .2|.1Standa|
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|00000160| 65 20 70 61 72 61 62 6f | 6c 61 20 70 61 73 73 65 |e parabo|la passe|
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|00000180| 69 6e 74 20 28 2d 32 2c | 20 31 29 2c 20 73 6f 20 |int (-2,| 1), so |
|00000190| 69 74 20 66 6f 6c 6c 6f | 77 73 20 74 68 61 74 20 |it follo|ws that |
|000001a0| 11 33 66 11 31 28 2d 32 | 29 20 3d 20 31 2e 0d 0a |.3f.1(-2|) = 1...|
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|000001c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 32 |        |      .2|
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|00000210| 3d 20 2d 32 2e 0d 0a 00 | 20 20 20 20 20 20 20 20 |= -2....|        |
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|000002a0| 20 3d 20 2d 32 28 11 33 | 78 20 11 31 2b 20 33 29 | = -2(.3|x .1+ 3)|
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|000003e0| 20 20 2b 20 33 20 20 20 | 20 20 20 20 20 20 20 11 |  + 3   |       .|
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|00000490| 20 3d 20 11 33 61 11 31 | 28 2d 32 20 2b 20 33 29 | = .3a.1|(-2 + 3)|
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|000004b0| 20 20 20 11 33 61 20 11 | 31 3d 20 2d 32 2e 0d 0a |   .3a .|1= -2...|
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|00000550| 33 78 20 11 31 2b 20 33 | 29 20 20 2b 20 33 2e 0d |3x .1+ 3|)  + 3..|
|00000560| 0a 00 00 17 4f 03 20 20 | 20 20 20 20 20 20 20 20 |....O.  |        |
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|00000580| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00000590| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 |        |       .|
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|00000630| 33 6b 11 31 29 20 3d 20 | 28 2d 33 2c 20 33 29 2c |3k.1) = |(-3, 3),|
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|000006b0| 20 21 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 20 | !...   |        |
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|000006d0| 37 0d 0b 00 11 31 12 30 | 20 20 20 20 20 20 20 20 |7....1.0|        |
|000006e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 |        |       .|
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|00000700| 11 33 78 11 31 29 20 3d | 20 11 33 61 11 31 28 11 |.3x.1) =| .3a.1(.|
|00000710| 33 78 20 11 31 2d 20 28 | 2d 33 29 29 20 20 2b 20 |3x .1- (|-3))  + |
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|000007c0| 20 77 65 20 6f 62 74 61 | 69 6e 20 31 20 3d 20 11 | we obta|in 1 = .|
|000007d0| 33 61 11 31 28 2d 32 20 | 2b 20 33 29 20 20 2b 20 |3a.1(-2 |+ 3)  + |
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|00000830| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 |        |       .|
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|00000880| 33 78 11 31 29 20 3d 20 | 2d 32 28 11 33 78 20 11 |3x.1) = |-2(.3x .|
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|00000cc0| 68 65 20 67 72 61 70 68 | 20 6f 66 20 11 33 68 11 |he graph| of .3h.|
|00000cd0| 31 2e 0d 0a 00 00 17 4f | 08 0d 0b 00 57 72 6f 6e |1......O|....Wron|
|00000ce0| 67 2e 20 20 46 69 72 73 | 74 2c 20 77 65 20 6e 65 |g.  Firs|t, we ne|
|00000cf0| 65 64 20 74 6f 20 77 72 | 69 74 65 20 74 68 65 20 |ed to wr|ite the |
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|00000d30| 11 31 28 11 33 78 11 31 | 29 20 3d 20 11 33 78 20 |.1(.3x.1|) = .3x |
|00000d40| 20 11 31 2d 20 38 11 33 | 78 20 11 31 2b 20 31 36 | .1- 8.3|x .1+ 16|
|00000d50| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00000d60| 20 20 11 32 12 31 47 69 | 76 65 6e 20 66 6f 72 6d |  .2.1Gi|ven form|
|00000d70| 12 30 0d 0a 00 20 20 20 | 20 20 20 20 20 20 20 20 |.0...   |        |
|00000d80| 20 20 20 32 0d 0b 00 20 | 20 20 20 20 11 31 3d 20 |   2... |    .1= |
|00000d90| 28 11 33 78 20 11 31 2d | 20 34 29 20 20 20 20 20 |(.3x .1-| 4)     |
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|00000db0| 20 20 11 32 12 31 53 74 | 61 6e 64 61 72 64 20 66 |  .2.1St|andard f|
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|00000e80| 20 61 6e 64 20 28 30 2c | 20 31 36 29 2e 0d 0a 00 | and (0,| 16)....|
|00000e90| 00 17 4f 04 0d 0b 00 53 | 6f 72 72 79 2c 20 6f 6e |..O....S|orry, on|
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|00000ec0| 54 72 79 20 61 67 61 69 | 6e 2e 0d 0a 00 00 17 4f |Try agai|n......O|
|00000ed0| 08 0d 0b 00 57 72 6f 6e | 67 2e 20 20 46 69 72 73 |....Wron|g.  Firs|
|00000ee0| 74 2c 20 77 65 20 6e 65 | 65 64 20 74 6f 20 77 72 |t, we ne|ed to wr|
|00000ef0| 69 74 65 20 74 68 65 20 | 66 75 6e 63 74 69 6f 6e |ite the |function|
|00000f00| 20 69 6e 20 73 74 61 6e | 64 61 72 64 20 66 6f 72 | in stan|dard for|
|00000f10| 6d 2e 12 30 0d 0a 00 20 | 20 20 20 20 20 20 20 20 |m..0... |        |
|00000f20| 11 32 32 0d 0b 00 11 33 | 66 11 31 28 11 33 78 11 |.22....3|f.1(.3x.|
|00000f30| 31 29 20 3d 20 2d 11 33 | 78 20 20 11 31 2b 20 32 |1) = -.3|x  .1+ 2|
|00000f40| 11 33 78 20 11 31 2b 20 | 35 20 20 20 20 20 20 20 |.3x .1+ |5       |
|00000f50| 20 20 20 20 20 20 20 20 | 20 20 20 11 32 12 31 47 |        |   .2.1G|
|00000f60| 69 76 65 6e 20 66 6f 72 | 6d 12 30 0d 0a 00 20 20 |iven for|m.0...  |
|00000f70| 20 20 20 20 20 20 20 20 | 32 0d 0b 00 20 20 20 20 |        |2...    |
|00000f80| 20 11 31 3d 20 2d 28 11 | 33 78 20 20 11 31 2d 20 | .1= -(.|3x  .1- |
|00000f90| 32 11 33 78 20 11 31 2b | 20 31 20 2d 20 31 29 20 |2.3x .1+| 1 - 1) |
|00000fa0| 2b 20 35 20 20 20 20 20 | 20 20 20 11 32 12 31 41 |+ 5     |   .2.1A|
|00000fb0| 64 64 20 61 6e 64 20 73 | 75 62 74 72 61 63 74 20 |dd and s|ubtract |
|00000fc0| 31 20 77 69 74 68 69 6e | 20 70 61 72 65 6e 74 68 |1 within| parenth|
|00000fd0| 65 73 65 73 12 30 0d 0a | 00 20 20 20 20 20 20 20 |eses.0..|.       |
|00000fe0| 20 20 20 32 0d 0b 00 20 | 20 20 20 20 11 31 3d 20 |   2... |    .1= |
|00000ff0| 2d 28 11 33 78 20 20 11 | 31 2d 20 32 11 33 78 20 |-(.3x  .|1- 2.3x |
|00001000| 11 31 2b 20 31 29 20 2d | 20 28 2d 31 29 20 2b 20 |.1+ 1) -| (-1) + |
|00001010| 35 20 20 20 20 20 11 32 | 12 31 52 65 67 72 6f 75 |5     .2|.1Regrou|
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|00001030| 20 20 20 20 20 20 20 20 | 20 20 20 32 0d 0b 00 20 |        |   2... |
|00001040| 20 20 20 20 11 31 3d 20 | 2d 28 11 33 78 20 11 31 |    .1= |-(.3x .1|
|00001050| 2d 20 31 29 20 20 2b 20 | 36 20 20 20 20 20 20 20 |- 1)  + |6       |
|00001060| 20 20 20 20 20 20 20 20 | 20 20 11 32 12 31 53 74 |        |  .2.1St|
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|00001080| 11 31 54 68 75 73 2c 20 | 74 68 65 20 67 72 61 70 |.1Thus, |the grap|
|00001090| 68 20 6f 66 20 11 33 66 | 20 11 31 6f 70 65 6e 73 |h of .3f| .1opens|
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|00001120| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.       |        |
|00001130| 20 20 20 20 20 11 34 44 | 32 0d 0b 00 11 31 61 74 |     .4D|2....1at|
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|00001150| 34 2b 20 53 20 11 31 36 | 2c 20 30 29 2e 0d 0a 00 |4+ S .16|, 0)....|
|00001160| 00 17 4f 08 0d 0b 00 57 | 72 6f 6e 67 2e 20 20 46 |..O....W|rong.  F|
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|00001190| 69 6f 6e 20 69 6e 20 73 | 74 61 6e 64 61 72 64 20 |ion in s|tandard |
|000011a0| 66 6f 72 6d 2e 12 30 0d | 0a 00 20 20 20 20 20 20 |form..0.|..      |
|000011b0| 20 20 20 11 32 32 0d 0b | 00 11 33 66 11 31 28 11 |   .22..|..3f.1(.|
|000011c0| 33 78 11 31 29 20 3d 20 | 2d 11 33 78 20 20 11 31 |3x.1) = |-.3x  .1|
|000011d0| 2b 20 32 11 33 78 20 11 | 31 2b 20 35 20 20 20 20 |+ 2.3x .|1+ 5    |
|000011e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 32 |        |      .2|
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|00001200| 00 20 20 20 20 20 20 20 | 20 20 20 32 0d 0b 00 20 |.       |   2... |
|00001210| 20 20 20 20 11 31 3d 20 | 2d 28 11 33 78 20 20 11 |    .1= |-(.3x  .|
|00001220| 31 2d 20 32 11 33 78 20 | 11 31 2b 20 31 20 2d 20 |1- 2.3x |.1+ 1 - |
|00001230| 31 29 20 2b 20 35 20 20 | 20 20 20 20 20 20 11 32 |1) + 5  |      .2|
|00001240| 12 31 41 64 64 20 61 6e | 64 20 73 75 62 74 72 61 |.1Add an|d subtra|
|00001250| 63 74 20 31 20 77 69 74 | 68 69 6e 20 70 61 72 65 |ct 1 wit|hin pare|
|00001260| 6e 74 68 65 73 65 73 12 | 30 0d 0a 00 20 20 20 20 |ntheses.|0...    |
|00001270| 20 20 20 20 20 20 32 0d | 0b 00 20 20 20 20 20 11 |      2.|..     .|
|00001280| 31 3d 20 2d 28 11 33 78 | 20 20 11 31 2d 20 32 11 |1= -(.3x|  .1- 2.|
|00001290| 33 78 20 11 31 2b 20 31 | 29 20 2d 20 28 2d 31 29 |3x .1+ 1|) - (-1)|
|000012a0| 20 2b 20 35 20 20 20 20 | 20 11 32 12 31 52 65 67 | + 5    | .2.1Reg|
|000012b0| 72 6f 75 70 20 74 65 72 | 6d 73 12 30 0d 0a 00 20 |roup ter|ms.0... |
|000012c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 32 0d |        |      2.|
|000012d0| 0b 00 20 20 20 20 20 11 | 31 3d 20 2d 28 11 33 78 |..     .|1= -(.3x|
|000012e0| 20 11 31 2d 20 31 29 20 | 20 2b 20 36 20 20 20 20 | .1- 1) | + 6    |
|000012f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 11 32 12 |        |     .2.|
|00001300| 31 53 74 61 6e 64 61 72 | 64 20 66 6f 72 6d 12 30 |1Standar|d form.0|
|00001310| 0d 0a 00 11 31 54 68 75 | 73 2c 20 74 68 65 20 67 |....1Thu|s, the g|
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|00001340| 68 20 76 65 72 74 65 78 | 20 28 31 2c 20 36 29 2e |h vertex| (1, 6).|
|00001350| 20 20 54 72 79 20 61 67 | 61 69 6e 2e 0d 0a 00 00 |  Try ag|ain.....|
|00001360| 17 4f 04 0d 0b 00 53 6f | 72 72 79 2c 20 6f 6e 65 |.O....So|rry, one|
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|000013a0| 0d 0b 00 52 69 67 68 74 | 2e 20 20 54 68 65 20 76 |...Right|.  The v|
|000013b0| 65 72 74 65 78 20 6f 66 | 20 11 33 68 20 11 31 69 |ertex of| .3h .1i|
|000013c0| 73 20 61 74 20 28 31 2f | 32 2c 20 32 30 29 2c 20 |s at (1/|2, 20), |
|000013d0| 61 6e 64 20 11 33 68 20 | 11 31 68 61 73 20 6f 6e |and .3h |.1has on|
|000013e0| 65 20 69 6e 74 65 72 63 | 65 70 74 20 61 74 20 28 |e interc|ept at (|
|000013f0| 30 2c 20 32 31 29 2e 0d | 0a 00 00 17 4f 08 0d 0b |0, 21)..|....O...|
|00001400| 00 57 72 6f 6e 67 2e 20 | 20 46 69 72 73 74 2c 20 |.Wrong. | First, |
|00001410| 77 65 20 6e 65 65 64 20 | 74 6f 20 77 72 69 74 65 |we need |to write|
|00001420| 20 74 68 65 20 66 75 6e | 63 74 69 6f 6e 20 69 6e | the fun|ction in|
|00001430| 20 73 74 61 6e 64 61 72 | 64 20 66 6f 72 6d 2e 12 | standar|d form..|
|00001440| 30 0d 0a 00 20 20 20 20 | 20 20 20 20 20 11 32 32 |0...    |     .22|
|00001450| 0d 0b 00 11 33 68 11 31 | 28 11 33 78 11 31 29 20 |....3h.1|(.3x.1) |
|00001460| 3d 20 34 11 33 78 20 20 | 11 31 2d 20 34 11 33 78 |= 4.3x  |.1- 4.3x|
|00001470| 20 11 31 2b 20 32 31 20 | 20 20 20 20 20 20 20 20 | .1+ 21 |        |
|00001480| 20 20 20 20 20 20 20 20 | 11 32 12 31 47 69 76 65 |        |.2.1Give|
|00001490| 6e 20 66 6f 72 6d 12 30 | 0d 0a 00 20 20 20 20 20 |n form.0|...     |
|000014a0| 20 20 20 20 20 32 20 20 | 20 20 20 20 20 11 31 31 |     2  |     .11|
|000014b0| 20 20 20 31 20 20 20 20 | 20 20 20 20 20 20 20 20 |   1    |        |
|000014c0| 20 20 11 32 12 31 20 20 | 20 20 20 20 20 20 20 20 |  .2.1  |        |
|000014d0| 20 20 20 20 20 20 20 31 | 20 20 20 20 20 20 20 20 |       1|        |
|000014e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000014f0| 20 12 30 0d 0b 00 20 20 | 20 20 20 11 31 3d 20 34 | .0...  |   .1= 4|
|00001500| 28 11 33 78 20 20 11 31 | 2d 20 11 33 78 20 11 31 |(.3x  .1|- .3x .1|
|00001510| 2b 20 11 34 32 20 11 31 | 2d 20 11 34 32 11 31 29 |+ .42 .1|- .42.1)|
|00001520| 20 2b 20 32 31 20 20 20 | 20 20 20 20 20 11 32 12 | + 21   |     .2.|
|00001530| 31 41 64 64 20 61 6e 64 | 20 73 75 62 74 72 61 63 |1Add and| subtrac|
|00001540| 74 20 11 34 32 20 11 32 | 77 69 74 68 69 6e 20 70 |t .42 .2|within p|
|00001550| 61 72 65 6e 74 68 65 73 | 65 73 12 30 0d 0b 00 20 |arenthes|es.0... |
|00001560| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001570| 20 11 31 34 20 20 20 34 | 20 20 20 20 20 20 20 20 | .14   4|        |
|00001580| 20 20 20 20 20 20 11 32 | 12 31 20 20 20 20 20 20 |      .2|.1      |
|00001590| 20 20 20 20 20 20 20 20 | 20 20 20 34 20 20 20 20 |        |   4    |
|000015a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000015b0| 20 20 12 30 0d 0a 00 20 | 20 20 20 20 20 20 20 20 |  .0... |        |
|000015c0| 20 32 20 20 20 20 20 20 | 20 11 31 31 0d 0b 00 20 | 2      | .11... |
|000015d0| 20 20 20 20 3d 20 34 28 | 11 33 78 20 20 11 31 2d |    = 4(|.3x  .1-|
|000015e0| 20 11 33 78 20 11 31 2b | 20 11 34 32 11 31 29 20 | .3x .1+| .42.1) |
|000015f0| 2d 20 31 20 2b 20 32 31 | 20 20 20 20 20 20 20 20 |- 1 + 21|        |
|00001600| 11 32 12 31 52 65 67 72 | 6f 75 70 20 74 65 72 6d |.2.1Regr|oup term|
|00001610| 73 12 30 0d 0b 00 20 20 | 20 20 20 20 20 20 20 20 |s.0...  |        |
|00001620| 20 20 20 20 20 20 20 20 | 11 31 34 0d 0a 00 20 20 |        |.14...  |
|00001630| 20 20 20 20 20 20 20 20 | 20 20 20 31 20 11 32 32 |        |   1 .22|
|00001640| 0d 0b 00 20 20 20 20 20 | 11 31 3d 20 34 28 11 33 |...     |.1= 4(.3|
|00001650| 78 20 11 31 2d 20 11 34 | 32 11 31 29 20 20 2b 20 |x .1- .4|2.1)  + |
|00001660| 32 30 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |20      |        |
|00001670| 20 20 11 32 12 31 53 74 | 61 6e 64 61 72 64 20 66 |  .2.1St|andard f|
|00001680| 6f 72 6d 12 30 0d 0b 00 | 20 20 20 20 20 20 20 20 |orm.0...|        |
|00001690| 20 20 20 20 20 11 31 32 | 0d 0a 00 54 68 75 73 2c |     .12|...Thus,|
|000016a0| 20 74 68 65 20 67 72 61 | 70 68 20 6f 66 20 11 33 | the gra|ph of .3|
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|000016c0| 20 77 69 74 68 20 76 65 | 72 74 65 78 20 28 31 2f | with ve|rtex (1/|
|000016d0| 32 2c 20 32 30 29 2e 20 | 20 54 72 79 20 61 67 61 |2, 20). | Try aga|
|000016e0| 69 6e 2e 0d 0a 00 00 17 | 4f 08 0d 0b 00 57 72 6f |in......|O....Wro|
|000016f0| 6e 67 2e 20 20 46 69 72 | 73 74 2c 20 77 65 20 6e |ng.  Fir|st, we n|
|00001700| 65 65 64 20 74 6f 20 77 | 72 69 74 65 20 74 68 65 |eed to w|rite the|
|00001710| 20 66 75 6e 63 74 69 6f | 6e 20 69 6e 20 73 74 61 | functio|n in sta|
|00001720| 6e 64 61 72 64 20 66 6f | 72 6d 2e 12 30 0d 0a 00 |ndard fo|rm..0...|
|00001730| 20 20 20 20 20 20 20 20 | 20 11 32 32 0d 0b 00 11 |        | .22....|
|00001740| 33 68 11 31 28 11 33 78 | 11 31 29 20 3d 20 34 11 |3h.1(.3x|.1) = 4.|
|00001750| 33 78 20 20 11 31 2d 20 | 34 11 33 78 20 11 31 2b |3x  .1- |4.3x .1+|
|00001760| 20 32 31 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | 21     |        |
|00001770| 20 20 20 20 11 32 12 31 | 47 69 76 65 6e 20 66 6f |    .2.1|Given fo|
|00001780| 72 6d 12 30 0d 0a 00 20 | 20 20 20 20 20 20 20 20 |rm.0... |        |
|00001790| 20 32 20 20 20 20 20 20 | 20 11 31 31 20 20 20 31 | 2      | .11   1|
|000017a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 32 |        |      .2|
|000017b0| 12 31 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.1      |        |
|000017c0| 20 20 20 31 20 20 20 20 | 20 20 20 20 20 20 20 20 |   1    |        |
|000017d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 12 30 0d |        |     .0.|
|000017e0| 0b 00 20 20 20 20 20 11 | 31 3d 20 34 28 11 33 78 |..     .|1= 4(.3x|
|000017f0| 20 20 11 31 2d 20 11 33 | 78 20 11 31 2b 20 11 34 |  .1- .3|x .1+ .4|
|00001800| 32 20 11 31 2d 20 11 34 | 32 11 31 29 20 2b 20 32 |2 .1- .4|2.1) + 2|
|00001810| 31 20 20 20 20 20 20 20 | 20 11 32 12 31 41 64 64 |1       | .2.1Add|
|00001820| 20 61 6e 64 20 73 75 62 | 74 72 61 63 74 20 11 34 | and sub|tract .4|
|00001830| 32 20 11 32 77 69 74 68 | 69 6e 20 70 61 72 65 6e |2 .2with|in paren|
|00001840| 74 68 65 73 65 73 12 30 | 20 0d 0b 00 20 20 20 20 |theses.0| ...    |
|00001850| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 31 |        |      .1|
|00001860| 34 20 20 20 34 20 20 20 | 20 20 20 20 20 20 20 20 |4   4   |        |
|00001870| 20 20 20 11 32 12 31 20 | 20 20 20 20 20 20 20 20 |   .2.1 |        |
|00001880| 20 20 20 20 20 20 20 20 | 34 20 20 20 20 20 20 20 |        |4       |
|00001890| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 12 |        |       .|
|000018a0| 30 0d 0a 00 20 20 20 20 | 20 20 20 20 20 20 32 20 |0...    |      2 |
|000018b0| 20 20 20 20 20 20 11 31 | 31 0d 0b 00 20 20 20 20 |      .1|1...    |
|000018c0| 20 3d 20 34 28 11 33 78 | 20 20 11 31 2d 20 11 33 | = 4(.3x|  .1- .3|
|000018d0| 78 20 11 31 2b 20 11 34 | 32 11 31 29 20 2d 20 31 |x .1+ .4|2.1) - 1|
|000018e0| 20 2b 20 32 31 20 20 20 | 20 20 20 20 20 11 32 12 | + 21   |     .2.|
|000018f0| 31 52 65 67 72 6f 75 70 | 20 74 65 72 6d 73 12 30 |1Regroup| terms.0|
|00001900| 0d 0b 00 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |...     |        |
|00001910| 20 20 20 20 20 11 31 34 | 0d 0a 00 20 20 20 20 20 |     .14|...     |
|00001920| 20 20 20 20 20 20 20 20 | 31 20 11 32 32 0d 0b 00 |        |1 .22...|
|00001930| 20 20 20 20 20 11 31 3d | 20 34 28 11 33 78 20 11 |     .1=| 4(.3x .|
|00001940| 31 2d 20 11 34 32 11 31 | 29 20 20 2b 20 32 30 20 |1- .42.1|)  + 20 |
|00001950| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 |        |       .|
|00001960| 32 12 31 53 74 61 6e 64 | 61 72 64 20 66 6f 72 6d |2.1Stand|ard form|
|00001970| 12 30 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 20 |.0...   |        |
|00001980| 20 20 11 31 32 0d 0a 00 | 54 68 75 73 2c 20 74 68 |  .12...|Thus, th|
|00001990| 65 20 67 72 61 70 68 20 | 6f 66 20 11 33 68 20 11 |e graph |of .3h .|
|000019a0| 31 6f 70 65 6e 73 20 75 | 70 77 61 72 64 20 77 69 |1opens u|pward wi|
|000019b0| 74 68 20 76 65 72 74 65 | 78 20 28 31 2f 32 2c 20 |th verte|x (1/2, |
|000019c0| 32 30 29 2e 20 20 54 72 | 79 20 61 67 61 69 6e 2e |20).  Tr|y again.|
|000019d0| 0d 0a 00 00 17 4f 04 0d | 0b 00 53 6f 72 72 79 2c |.....O..|..Sorry,|
|000019e0| 20 6f 6e 65 20 6f 66 20 | 74 68 65 73 65 20 61 6e | one of |these an|
|000019f0| 73 77 65 72 73 20 69 73 | 20 63 6f 72 72 65 63 74 |swers is| correct|
|00001a00| 2e 20 20 54 72 79 20 61 | 67 61 69 6e 2e 20 0d 0a |.  Try a|gain. ..|
|00001a10| 00 00 17 4f 09 20 20 20 | 20 20 20 20 20 20 20 20 |...O.   |        |
|00001a20| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001a30| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001a40| 20 20 20 20 20 20 20 20 | 20 11 32 32 0d 0b 00 11 |        | .22....|
|00001a50| 31 57 72 6f 6e 67 2e 20 | 20 54 68 65 20 66 75 6e |1Wrong. | The fun|
|00001a60| 63 74 69 6f 6e 20 68 61 | 73 20 74 68 65 20 66 6f |ction ha|s the fo|
|00001a70| 72 6d 20 6f 66 20 11 33 | 66 11 31 28 11 33 78 11 |rm of .3|f.1(.3x.|
|00001a80| 31 29 20 3d 20 11 33 61 | 11 31 28 11 33 78 20 11 |1) = .3a|.1(.3x .|
|00001a90| 31 2d 20 11 33 68 11 31 | 29 20 20 2b 20 11 33 6b |1- .3h.1|)  + .3k|
|00001aa0| 11 31 2e 20 20 54 68 65 | 20 76 65 72 74 65 78 20 |.1.  The| vertex |
|00001ab0| 69 73 0d 0a 00 28 2d 31 | 2c 20 33 29 2c 20 73 6f |is...(-1|, 3), so|
|00001ac0| 20 11 33 68 20 11 31 3d | 20 2d 31 20 61 6e 64 20 | .3h .1=| -1 and |
|00001ad0| 11 33 6b 20 11 31 3d 20 | 33 2e 20 20 4e 6f 77 2c |.3k .1= |3.  Now,|
|00001ae0| 20 75 73 65 20 74 68 65 | 20 66 61 63 74 20 74 68 | use the| fact th|
|00001af0| 61 74 20 11 33 66 11 31 | 28 32 29 20 3d 20 31 20 |at .3f.1|(2) = 1 |
|00001b00| 74 6f 20 66 69 6e 64 20 | 11 33 61 11 31 2e 12 30 |to find |.3a.1..0|
|00001b10| 0d 0a 00 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |...     |        |
|00001b20| 20 20 20 20 20 20 20 11 | 32 32 0d 0b 00 20 20 20 |       .|22...   |
|00001b30| 20 20 11 31 31 20 3d 20 | 11 33 61 11 31 28 32 20 |  .11 = |.3a.1(2 |
|00001b40| 2d 20 28 2d 31 29 29 20 | 20 2b 20 33 0d 0a 00 20 |- (-1)) | + 3... |
|00001b50| 20 20 20 2d 32 20 3d 20 | 39 11 33 61 0d 0a 00 20 |   -2 = |9.3a... |
|00001b60| 20 20 20 20 11 31 32 0d | 0b 00 20 20 20 20 2d 11 |    .12.|..    -.|
|00001b70| 34 32 20 11 31 3d 20 11 | 33 61 0d 0b 00 20 20 20 |42 .1= .|3a...   |
|00001b80| 20 20 11 31 39 0d 0a 00 | 20 20 20 20 20 20 20 20 |  .19...|        |
|00001b90| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001ba0| 20 20 20 20 20 20 32 20 | 20 20 20 20 20 20 11 32 |      2 |      .2|
|00001bb0| 32 0d 0b 00 11 31 54 68 | 75 73 2c 20 74 68 65 20 |2....1Th|us, the |
|00001bc0| 66 75 6e 63 74 69 6f 6e | 20 69 73 20 11 33 66 11 |function| is .3f.|
|00001bd0| 31 28 11 33 78 11 31 29 | 20 3d 20 2d 11 34 32 11 |1(.3x.1)| = -.42.|
|00001be0| 31 28 11 33 78 20 11 31 | 2b 20 31 29 20 20 2b 20 |1(.3x .1|+ 1)  + |
|00001bf0| 33 2e 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 20 |3....   |        |
|00001c00| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001c10| 20 20 20 39 0d 0a 00 00 | 17 4f 09 20 20 20 20 20 |   9....|.O.     |
|00001c20| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001c30| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001c40| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 |        |       .|
|00001c50| 32 32 0d 0b 00 11 31 57 | 72 6f 6e 67 2e 20 20 54 |22....1W|rong.  T|
|00001c60| 68 65 20 66 75 6e 63 74 | 69 6f 6e 20 68 61 73 20 |he funct|ion has |
|00001c70| 74 68 65 20 66 6f 72 6d | 20 6f 66 20 11 33 66 11 |the form| of .3f.|
|00001c80| 31 28 11 33 78 11 31 29 | 20 3d 20 11 33 61 11 31 |1(.3x.1)| = .3a.1|
|00001c90| 28 11 33 78 20 11 31 2d | 20 11 33 68 11 31 29 20 |(.3x .1-| .3h.1) |
|00001ca0| 20 2b 20 11 33 6b 11 31 | 2e 20 20 54 68 65 20 76 | + .3k.1|.  The v|
|00001cb0| 65 72 74 65 78 20 69 73 | 0d 0a 00 28 2d 31 2c 20 |ertex is|...(-1, |
|00001cc0| 33 29 2c 20 73 6f 20 11 | 33 68 20 11 31 3d 20 2d |3), so .|3h .1= -|
|00001cd0| 31 20 61 6e 64 20 11 33 | 6b 20 11 31 3d 20 33 2e |1 and .3|k .1= 3.|
|00001ce0| 20 20 4e 6f 77 2c 20 75 | 73 65 20 74 68 65 20 66 |  Now, u|se the f|
|00001cf0| 61 63 74 20 74 68 61 74 | 20 11 33 66 11 31 28 32 |act that| .3f.1(2|
|00001d00| 29 20 3d 20 31 20 74 6f | 20 66 69 6e 64 20 11 33 |) = 1 to| find .3|
|00001d10| 61 11 31 2e 12 30 0d 0a | 00 20 20 20 20 20 20 20 |a.1..0..|.       |
|00001d20| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 11 32 32 |        |     .22|
|00001d30| 0d 0b 00 20 20 20 20 20 | 11 31 31 20 3d 20 11 33 |...     |.11 = .3|
|00001d40| 61 11 31 28 32 20 2d 20 | 28 2d 31 29 29 20 20 2b |a.1(2 - |(-1))  +|
|00001d50| 20 33 0d 0a 00 20 20 20 | 20 2d 32 20 3d 20 39 11 | 3...   | -2 = 9.|
|00001d60| 33 61 0d 0a 00 20 20 20 | 20 20 11 31 32 0d 0b 00 |3a...   |  .12...|
|00001d70| 20 20 20 20 2d 11 34 32 | 20 11 31 3d 20 11 33 61 |    -.42| .1= .3a|
|00001d80| 0d 0b 00 20 20 20 20 20 | 11 31 39 0d 0a 00 20 20 |...     |.19...  |
|00001d90| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001da0| 20 20 20 20 20 20 20 20 | 20 20 20 20 32 20 20 20 |        |    2   |
|00001db0| 20 20 20 20 11 32 32 0d | 0b 00 11 31 54 68 75 73 |    .22.|...1Thus|
|00001dc0| 2c 20 74 68 65 20 66 75 | 6e 63 74 69 6f 6e 20 69 |, the fu|nction i|
|00001dd0| 73 20 11 33 66 11 31 28 | 11 33 78 11 31 29 20 3d |s .3f.1(|.3x.1) =|
|00001de0| 20 2d 11 34 32 11 31 28 | 11 33 78 20 11 31 2b 20 | -.42.1(|.3x .1+ |
|00001df0| 31 29 20 20 2b 20 33 2e | 0d 0b 00 20 20 20 20 20 |1)  + 3.|...     |
|00001e00| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001e10| 20 20 20 20 20 20 20 20 | 20 39 0d 0a 00 00 17 4f |        | 9.....O|
|00001e20| 04 0d 0b 00 20 20 20 20 | 20 20 20 20 20 20 20 20 |....    |        |
|00001e30| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001e40| 20 20 20 20 32 20 20 20 | 20 20 20 20 11 32 32 0d |    2   |    .22.|
|00001e50| 0b 00 11 31 52 69 67 68 | 74 2e 20 20 54 68 65 20 |...1Righ|t.  The |
|00001e60| 66 75 6e 63 74 69 6f 6e | 20 69 73 20 11 33 66 11 |function| is .3f.|
|00001e70| 31 28 11 33 78 11 31 29 | 20 3d 20 2d 11 34 32 11 |1(.3x.1)| = -.42.|
|00001e80| 31 28 11 33 78 20 11 31 | 2b 20 31 29 20 20 2b 20 |1(.3x .1|+ 1)  + |
|00001e90| 33 2e 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 20 |3....   |        |
|00001ea0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001eb0| 20 20 20 20 20 39 0d 0a | 00 00 17 4f 03 0d 0b 00 |     9..|...O....|
|00001ec0| 53 6f 72 72 79 2c 20 74 | 68 65 72 65 20 69 73 20 |Sorry, t|here is |
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|00001ef0| 65 64 20 45 78 61 6d 70 | 6c 65 20 32 20 61 6e 64 |ed Examp|le 2 and|
|00001f00| 20 74 72 79 20 61 67 61 | 69 6e 2e 0d 0a 00 00 17 | try aga|in......|
|00001f10| 4f 0b 0d 0b 00 57 72 6f | 6e 67 2e 20 20 54 68 65 |O....Wro|ng.  The|
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|00001f30| 20 6f 66 20 74 68 65 20 | 74 77 6f 20 63 6f 72 72 | of the |two corr|
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|00001f60| 11 33 79 11 31 2e 0d 0a | 00 54 68 75 73 2c 20 74 |.3y.1...|.Thus, t|
|00001f70| 68 65 20 61 72 65 61 20 | 6f 66 20 74 68 65 20 74 |he area |of the t|
|00001f80| 77 6f 20 63 6f 72 72 61 | 6c 73 20 69 73 20 67 69 |wo corra|ls is gi|
|00001f90| 76 65 6e 20 62 79 20 11 | 33 41 20 11 31 3d 20 28 |ven by .|3A .1= (|
|00001fa0| 32 11 33 78 11 31 29 11 | 33 79 11 31 2e 20 20 53 |2.3x.1).|3y.1.  S|
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|00001fc0| 6f 62 74 61 69 6e 20 61 | 20 71 75 61 64 72 61 74 |obtain a| quadrat|
|00001fd0| 69 63 20 65 71 75 61 74 | 69 6f 6e 2c 20 77 65 20 |ic equat|ion, we |
|00001fe0| 6e 65 65 64 20 74 6f 20 | 72 65 77 72 69 74 65 20 |need to |rewrite |
|00001ff0| 11 33 41 20 11 31 69 6e | 20 74 65 72 6d 73 20 6f |.3A .1in| terms o|
|00002000| 66 20 6f 6e 65 20 76 61 | 72 69 61 62 6c 65 0d 0a |f one va|riable..|
|00002010| 00 28 65 69 74 68 65 72 | 20 11 33 78 20 11 31 6f |.(either| .3x .1o|
|00002020| 72 20 11 33 79 11 31 29 | 2e 20 20 54 68 65 20 72 |r .3y.1)|.  The r|
|00002030| 61 6e 63 68 65 72 20 68 | 61 73 20 32 30 30 20 66 |ancher h|as 200 f|
|00002040| 65 65 74 20 6f 66 20 66 | 65 6e 63 65 2c 20 77 69 |eet of f|ence, wi|
|00002050| 74 68 20 34 20 73 69 64 | 65 73 20 11 33 78 20 11 |th 4 sid|es .3x .|
|00002060| 31 66 65 65 74 0d 0a 00 | 20 20 20 20 20 20 20 20 |1feet...|        |
|00002070| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002080| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002090| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000020a0| 20 20 20 32 30 30 20 2d | 20 34 11 33 78 0d 0b 00 |   200 -| 4.3x...|
|000020b0| 11 31 6c 6f 6e 67 20 61 | 6e 64 20 33 20 73 69 64 |.1long a|nd 3 sid|
|000020c0| 65 73 20 11 33 79 20 11 | 31 66 65 65 74 20 6c 6f |es .3y .|1feet lo|
|000020d0| 6e 67 2e 20 20 54 68 75 | 73 2c 20 34 11 33 78 20 |ng.  Thu|s, 4.3x |
|000020e0| 11 31 2b 20 33 11 33 79 | 20 11 31 3d 20 32 30 30 |.1+ 3.3y| .1= 200|
|000020f0| 2c 20 6f 72 20 11 33 79 | 20 11 31 3d 20 11 34 32 |, or .3y| .1= .42|
|00002100| 32 32 32 32 32 32 32 11 | 31 2e 20 20 0d 0b 00 20 |2222222.|1.  ... |
|00002110| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002120| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002130| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002140| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 33 0d |        |      3.|
|00002150| 0b 00 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |..      |        |
|00002160| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002170| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002180| 20 20 20 20 20 20 20 20 | 20 20 20 11 34 28 20 20 |        |   .4(  |
|00002190| 20 20 20 20 20 20 29 0d | 0b 00 20 20 20 20 20 20 |      ).|..      |
|000021a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000021b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000021c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000021d0| 20 20 20 21 11 31 32 30 | 30 20 2d 20 34 11 33 78 |   !.120|0 - 4.3x|
|000021e0| 11 34 21 0d 0b 00 11 31 | 53 75 62 73 74 69 74 75 |.4!....1|Substitu|
|000021f0| 74 69 6e 67 20 69 6e 74 | 6f 20 6f 75 72 20 65 71 |ting int|o our eq|
|00002200| 75 61 74 69 6f 6e 20 66 | 6f 72 20 61 72 65 61 2c |uation f|or area,|
|00002210| 20 77 65 20 6f 62 74 61 | 69 6e 20 11 33 41 20 11 | we obta|in .3A .|
|00002220| 31 3d 20 32 11 33 78 11 | 34 21 32 32 32 32 32 32 |1= 2.3x.|4!222222|
|00002230| 32 32 21 11 31 2e 0d 0b | 00 20 20 20 20 20 20 20 |22!.1...|.       |
|00002240| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002250| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002260| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002270| 20 20 11 34 21 20 20 20 | 20 11 31 33 20 20 20 11 |  .4!   | .13   .|
|00002280| 34 21 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 20 |4!...   |        |
|00002290| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000022a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000022b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 39 20 |        |      9 |
|000022c0| 20 20 20 20 20 20 20 30 | 0d 0a 00 11 31 57 72 69 |       0|....1Wri|
|000022d0| 74 65 20 11 33 41 20 11 | 31 69 6e 20 73 74 61 6e |te .3A .|1in stan|
|000022e0| 64 61 72 64 20 66 6f 72 | 6d 20 61 6e 64 20 66 69 |dard for|m and fi|
|000022f0| 6e 64 20 11 33 41 11 31 | 27 73 20 76 65 72 74 65 |nd .3A.1|'s verte|
|00002300| 78 20 74 6f 20 6f 62 74 | 61 69 6e 20 74 68 65 20 |x to obt|ain the |
|00002310| 72 69 67 68 74 20 61 6e | 73 77 65 72 2e 0d 0a 00 |right an|swer....|
|00002320| 00 17 4f 0b 0d 0b 00 57 | 72 6f 6e 67 2e 20 20 54 |..O....W|rong.  T|
|00002330| 68 65 20 63 6f 6d 62 69 | 6e 65 64 20 6c 65 6e 67 |he combi|ned leng|
|00002340| 74 68 20 6f 66 20 74 68 | 65 20 74 77 6f 20 63 6f |th of th|e two co|
|00002350| 72 72 61 6c 73 20 69 73 | 20 32 11 33 78 11 31 2c |rrals is| 2.3x.1,|
|00002360| 20 61 6e 64 20 74 68 65 | 20 77 69 64 74 68 20 69 | and the| width i|
|00002370| 73 20 11 33 79 11 31 2e | 0d 0a 00 54 68 75 73 2c |s .3y.1.|...Thus,|
|00002380| 20 74 68 65 20 61 72 65 | 61 20 6f 66 20 74 68 65 | the are|a of the|
|00002390| 20 74 77 6f 20 63 6f 72 | 72 61 6c 73 20 69 73 20 | two cor|rals is |
|000023a0| 67 69 76 65 6e 20 62 79 | 20 11 33 41 20 11 31 3d |given by| .3A .1=|
|000023b0| 20 28 32 11 33 78 11 31 | 29 11 33 79 11 31 2e 20 | (2.3x.1|).3y.1. |
|000023c0| 20 53 6f 20 74 68 61 74 | 20 77 65 20 63 61 6e 0d | So that| we can.|
|000023d0| 0a 00 6f 62 74 61 69 6e | 20 61 20 71 75 61 64 72 |..obtain| a quadr|
|000023e0| 61 74 69 63 20 65 71 75 | 61 74 69 6f 6e 2c 20 77 |atic equ|ation, w|
|000023f0| 65 20 6e 65 65 64 20 74 | 6f 20 72 65 77 72 69 74 |e need t|o rewrit|
|00002400| 65 20 11 33 41 20 11 31 | 69 6e 20 74 65 72 6d 73 |e .3A .1|in terms|
|00002410| 20 6f 66 20 6f 6e 65 20 | 76 61 72 69 61 62 6c 65 | of one |variable|
|00002420| 0d 0a 00 28 65 69 74 68 | 65 72 20 11 33 78 20 11 |...(eith|er .3x .|
|00002430| 31 6f 72 20 11 33 79 11 | 31 29 2e 20 20 54 68 65 |1or .3y.|1).  The|
|00002440| 20 72 61 6e 63 68 65 72 | 20 68 61 73 20 32 30 30 | rancher| has 200|
|00002450| 20 66 65 65 74 20 6f 66 | 20 66 65 6e 63 65 2c 20 | feet of| fence, |
|00002460| 77 69 74 68 20 34 20 73 | 69 64 65 73 20 11 33 78 |with 4 s|ides .3x|
|00002470| 20 11 31 66 65 65 74 0d | 0a 00 20 20 20 20 20 20 | .1feet.|..      |
|00002480| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002490| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000024a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000024b0| 20 20 20 20 20 32 30 30 | 20 2d 20 34 11 33 78 0d |     200| - 4.3x.|
|000024c0| 0b 00 11 31 6c 6f 6e 67 | 20 61 6e 64 20 33 20 73 |...1long| and 3 s|
|000024d0| 69 64 65 73 20 11 33 79 | 20 11 31 66 65 65 74 20 |ides .3y| .1feet |
|000024e0| 6c 6f 6e 67 2e 20 20 54 | 68 75 73 2c 20 34 11 33 |long.  T|hus, 4.3|
|000024f0| 78 20 11 31 2b 20 33 11 | 33 79 20 11 31 3d 20 32 |x .1+ 3.|3y .1= 2|
|00002500| 30 30 2c 20 6f 72 20 11 | 33 79 20 11 31 3d 20 11 |00, or .|3y .1= .|
|00002510| 34 32 32 32 32 32 32 32 | 32 11 31 2e 20 20 0d 0b |42222222|2.1.  ..|
|00002520| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.       |        |
|00002530| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
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|00002560| 33 0d 0b 00 20 20 20 20 | 20 20 20 20 20 20 20 20 |3...    |        |
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|00002590| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 11 34 28 |        |     .4(|
|000025a0| 20 20 20 20 20 20 20 20 | 29 0d 0b 00 20 20 20 20 |        |)...    |
|000025b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
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|000025d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000025e0| 20 20 20 20 20 21 11 31 | 32 30 30 20 2d 20 34 11 |     !.1|200 - 4.|
|000025f0| 33 78 11 34 21 0d 0b 00 | 11 31 53 75 62 73 74 69 |3x.4!...|.1Substi|
|00002600| 74 75 74 69 6e 67 20 69 | 6e 74 6f 20 6f 75 72 20 |tuting i|nto our |
|00002610| 65 71 75 61 74 69 6f 6e | 20 66 6f 72 20 61 72 65 |equation| for are|
|00002620| 61 2c 20 77 65 20 6f 62 | 74 61 69 6e 20 11 33 41 |a, we ob|tain .3A|
|00002630| 20 11 31 3d 20 32 11 33 | 78 11 34 21 32 32 32 32 | .1= 2.3|x.4!2222|
|00002640| 32 32 32 32 21 11 31 2e | 0d 0b 00 20 20 20 20 20 |2222!.1.|...     |
|00002650| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002660| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002670| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002680| 20 20 20 20 11 34 21 20 | 20 20 20 11 31 33 20 20 |    .4! |   .13  |
|00002690| 20 11 34 21 0d 0b 00 20 | 20 20 20 20 20 20 20 20 | .4!... |        |
|000026a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
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|000026d0| 39 20 20 20 20 20 20 20 | 20 30 0d 0a 00 11 31 57 |9       | 0....1W|
|000026e0| 72 69 74 65 20 11 33 41 | 20 11 31 69 6e 20 73 74 |rite .3A| .1in st|
|000026f0| 61 6e 64 61 72 64 20 66 | 6f 72 6d 20 61 6e 64 20 |andard f|orm and |
|00002700| 66 69 6e 64 20 11 33 41 | 11 31 27 73 20 76 65 72 |find .3A|.1's ver|
|00002710| 74 65 78 20 74 6f 20 6f | 62 74 61 69 6e 20 74 68 |tex to o|btain th|
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|00002730| 0a 00 00 17 4f 04 20 20 | 20 20 20 20 20 20 20 20 |....O.  |        |
|00002740| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002750| 20 20 20 20 20 20 20 20 | 20 31 0d 0b 00 52 69 67 |        | 1...Rig|
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|00002770| 3d 20 32 35 20 66 65 65 | 74 20 61 6e 64 20 11 33 |= 25 fee|t and .3|
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|00002790| 65 74 2c 20 74 68 65 20 | 64 69 6d 65 6e 73 69 6f |et, the |dimensio|
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|000027b0| 6d 20 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 20 |m ...   |        |
|000027c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000027d0| 20 20 20 20 20 20 20 20 | 33 0d 0a 00 20 20 20 20 |        |3...    |
|000027e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000027f0| 20 20 20 20 20 20 20 20 | 20 20 20 31 0d 0b 00 65 |        |   1...e|
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|00002810| 20 35 30 20 66 65 65 74 | 20 62 79 20 33 33 11 34 | 50 feet| by 33.4|
|00002820| 32 20 11 31 66 65 65 74 | 2e 0d 0b 00 20 20 20 20 |2 .1feet|....    |
|00002830| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002840| 20 20 20 20 20 20 20 20 | 20 20 20 33 0d 0a 00 00 |        |   3....|
|00002850| 17 4f 0b 0d 0b 00 57 72 | 6f 6e 67 2e 20 20 54 68 |.O....Wr|ong.  Th|
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|00002870| 68 20 6f 66 20 74 68 65 | 20 74 77 6f 20 63 6f 72 |h of the| two cor|
|00002880| 72 61 6c 73 20 69 73 20 | 32 11 33 78 11 31 2c 20 |rals is |2.3x.1, |
|00002890| 61 6e 64 20 74 68 65 20 | 77 69 64 74 68 20 69 73 |and the |width is|
|000028a0| 20 11 33 79 11 31 2e 0d | 0a 00 54 68 75 73 2c 20 | .3y.1..|..Thus, |
|000028b0| 74 68 65 20 61 72 65 61 | 20 6f 66 20 74 68 65 20 |the area| of the |
|000028c0| 74 77 6f 20 63 6f 72 72 | 61 6c 73 20 69 73 20 67 |two corr|als is g|
|000028d0| 69 76 65 6e 20 62 79 20 | 11 33 41 20 11 31 3d 20 |iven by |.3A .1= |
|000028e0| 28 32 11 33 78 11 31 29 | 11 33 79 11 31 2e 20 20 |(2.3x.1)|.3y.1.  |
|000028f0| 53 6f 20 74 68 61 74 20 | 77 65 20 63 61 6e 0d 0a |So that |we can..|
|00002900| 00 6f 62 74 61 69 6e 20 | 61 20 71 75 61 64 72 61 |.obtain |a quadra|
|00002910| 74 69 63 20 65 71 75 61 | 74 69 6f 6e 2c 20 77 65 |tic equa|tion, we|
|00002920| 20 6e 65 65 64 20 74 6f | 20 72 65 77 72 69 74 65 | need to| rewrite|
|00002930| 20 11 33 41 20 11 31 69 | 6e 20 74 65 72 6d 73 20 | .3A .1i|n terms |
|00002940| 6f 66 20 6f 6e 65 20 76 | 61 72 69 61 62 6c 65 0d |of one v|ariable.|
|00002950| 0a 00 28 65 69 74 68 65 | 72 20 11 33 78 20 11 31 |..(eithe|r .3x .1|
|00002960| 6f 72 20 11 33 79 11 31 | 29 2e 20 20 54 68 65 20 |or .3y.1|).  The |
|00002970| 72 61 6e 63 68 65 72 20 | 68 61 73 20 32 30 30 20 |rancher |has 200 |
|00002980| 66 65 65 74 20 6f 66 20 | 66 65 6e 63 65 2c 20 77 |feet of |fence, w|
|00002990| 69 74 68 20 34 20 73 69 | 64 65 73 20 11 33 78 20 |ith 4 si|des .3x |
|000029a0| 11 31 66 65 65 74 0d 0a | 00 20 20 20 20 20 20 20 |.1feet..|.       |
|000029b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
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|000029d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000029e0| 20 20 20 20 32 30 30 20 | 2d 20 34 11 33 78 0d 0b |    200 |- 4.3x..|
|000029f0| 00 11 31 6c 6f 6e 67 20 | 61 6e 64 20 33 20 73 69 |..1long |and 3 si|
|00002a00| 64 65 73 20 11 33 79 20 | 11 31 66 65 65 74 20 6c |des .3y |.1feet l|
|00002a10| 6f 6e 67 2e 20 20 54 68 | 75 73 2c 20 34 11 33 78 |ong.  Th|us, 4.3x|
|00002a20| 20 11 31 2b 20 33 11 33 | 79 20 11 31 3d 20 32 30 | .1+ 3.3|y .1= 20|
|00002a30| 30 2c 20 6f 72 20 11 33 | 79 20 11 31 3d 20 11 34 |0, or .3|y .1= .4|
|00002a40| 32 32 32 32 32 32 32 32 | 11 31 2e 20 20 0d 0b 00 |22222222|.1.  ...|
|00002a50| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
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|00002a80| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 33 |        |       3|
|00002a90| 0d 0b 00 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |...     |        |
|00002aa0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002ab0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002ac0| 20 20 20 20 20 20 20 20 | 20 20 20 20 11 34 28 20 |        |    .4( |
|00002ad0| 20 20 20 20 20 20 20 29 | 0d 0b 00 20 20 20 20 20 |       )|...     |
|00002ae0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002af0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002b00| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002b10| 20 20 20 20 21 11 31 32 | 30 30 20 2d 20 34 11 33 |    !.12|00 - 4.3|
|00002b20| 78 11 34 21 0d 0b 00 11 | 31 53 75 62 73 74 69 74 |x.4!....|1Substit|
|00002b30| 75 74 69 6e 67 20 69 6e | 74 6f 20 6f 75 72 20 65 |uting in|to our e|
|00002b40| 71 75 61 74 69 6f 6e 20 | 66 6f 72 20 61 72 65 61 |quation |for area|
|00002b50| 2c 20 77 65 20 6f 62 74 | 61 69 6e 20 11 33 41 20 |, we obt|ain .3A |
|00002b60| 11 31 3d 20 32 11 33 78 | 11 34 21 32 32 32 32 32 |.1= 2.3x|.4!22222|
|00002b70| 32 32 32 21 11 31 2e 0d | 0b 00 20 20 20 20 20 20 |222!.1..|..      |
|00002b80| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002b90| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002ba0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002bb0| 20 20 20 11 34 21 20 20 | 20 20 11 31 33 20 20 20 |   .4!  |  .13   |
|00002bc0| 11 34 21 0d 0b 00 20 20 | 20 20 20 20 20 20 20 20 |.4!...  |        |
|00002bd0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002be0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002bf0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 39 |        |       9|
|00002c00| 20 20 20 20 20 20 20 20 | 30 0d 0a 00 11 31 57 72 |        |0....1Wr|
|00002c10| 69 74 65 20 11 33 41 20 | 11 31 69 6e 20 73 74 61 |ite .3A |.1in sta|
|00002c20| 6e 64 61 72 64 20 66 6f | 72 6d 20 61 6e 64 20 66 |ndard fo|rm and f|
|00002c30| 69 6e 64 20 11 33 41 11 | 31 27 73 20 76 65 72 74 |ind .3A.|1's vert|
|00002c40| 65 78 20 74 6f 20 6f 62 | 74 61 69 6e 20 74 68 65 |ex to ob|tain the|
|00002c50| 20 72 69 67 68 74 20 61 | 6e 73 77 65 72 2e 0d 0a | right a|nswer...|
|00002c60| 00 00 17 4f 09 0d 0b 00 | 57 72 6f 6e 67 2e 20 20 |...O....|Wrong.  |
|00002c70| 53 69 6e 63 65 20 74 68 | 65 20 70 61 72 61 62 6f |Since th|e parabo|
|00002c80| 6c 61 20 68 61 73 20 61 | 20 76 65 72 74 65 78 20 |la has a| vertex |
|00002c90| 61 74 20 28 11 33 68 11 | 31 2c 20 11 33 6b 11 31 |at (.3h.|1, .3k.1|
|00002ca0| 29 20 3d 20 28 32 2c 20 | 30 29 2c 20 74 68 65 20 |) = (2, |0), the |
|00002cb0| 65 71 75 61 74 69 6f 6e | 20 0d 0a 00 6d 75 73 74 |equation| ...must|
|00002cc0| 20 68 61 76 65 20 74 68 | 65 20 66 6f 6c 6c 6f 77 | have th|e follow|
|00002cd0| 69 6e 67 20 66 6f 72 6d | 2e 12 38 0d 0a 00 20 20 |ing form|..8...  |
|00002ce0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002cf0| 11 33 68 20 20 20 20 20 | 6b 0d 0a 00 20 20 20 20 |.3h     |k...    |
|00002d00| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 34 |        |      .4|
|00002d10| 21 20 20 20 20 20 21 0d | 0b 00 20 20 20 20 20 20 |!     !.|..      |
|00002d20| 20 20 20 20 20 20 20 20 | 20 20 20 20 37 20 20 20 |        |    7   |
|00002d30| 20 20 37 0d 0b 00 11 31 | 12 30 20 20 20 20 20 20 |  7....1|.0      |
|00002d40| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 32 |        |      .2|
|00002d50| 32 0d 0b 00 20 20 20 20 | 20 11 33 66 11 31 28 11 |2...    | .3f.1(.|
|00002d60| 33 78 11 31 29 20 3d 20 | 11 33 61 11 31 28 11 33 |3x.1) = |.3a.1(.3|
|00002d70| 78 20 11 31 2d 20 32 29 | 20 20 2b 20 30 20 20 20 |x .1- 2)|  + 0   |
|00002d80| 20 20 20 20 20 20 20 11 | 32 12 31 53 74 61 6e 64 |       .|2.1Stand|
|00002d90| 61 72 64 20 66 6f 72 6d | 12 30 0d 0a 00 11 31 54 |ard form|.0....1T|
|00002da0| 68 65 20 70 61 72 61 62 | 6f 6c 61 20 70 61 73 73 |he parab|ola pass|
|00002db0| 65 73 20 74 68 72 6f 75 | 67 68 20 74 68 65 20 70 |es throu|gh the p|
|00002dc0| 6f 69 6e 74 20 28 30 2c | 20 34 29 2c 20 73 6f 20 |oint (0,| 4), so |
|00002dd0| 69 74 20 66 6f 6c 6c 6f | 77 73 20 74 68 61 74 20 |it follo|ws that |
|00002de0| 11 33 66 11 31 28 30 29 | 20 3d 20 34 2e 0d 0a 00 |.3f.1(0)| = 4....|
|00002df0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002e00| 20 20 20 20 20 20 20 20 | 20 20 20 20 11 32 32 0d |        |    .22.|
|00002e10| 0b 00 11 31 54 68 75 73 | 2c 20 77 65 20 6f 62 74 |...1Thus|, we obt|
|00002e20| 61 69 6e 20 34 20 3d 20 | 11 33 61 11 31 28 30 20 |ain 4 = |.3a.1(0 |
|00002e30| 2d 20 32 29 20 20 20 20 | 20 20 11 34 35 35 36 20 |- 2)    |  .4556 |
|00002e40| 20 20 20 20 11 33 61 20 | 11 31 3d 20 31 2e 0d 0a |    .3a |.1= 1...|
|00002e50| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.       |        |
|00002e60| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002e70| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002e80| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002e90| 20 11 32 32 0d 0b 00 11 | 31 54 68 69 73 20 69 6d | .22....|1This im|
|00002ea0| 70 6c 69 65 73 20 74 68 | 61 74 20 74 68 65 20 65 |plies th|at the e|
|00002eb0| 71 75 61 74 69 6f 6e 20 | 6f 66 20 74 68 65 20 70 |quation |of the p|
|00002ec0| 61 72 61 62 6f 6c 61 20 | 69 73 20 11 33 66 11 31 |arabola |is .3f.1|
|00002ed0| 28 11 33 78 11 31 29 20 | 3d 20 28 11 33 78 20 11 |(.3x.1) |= (.3x .|
|00002ee0| 31 2d 20 32 29 20 2e 0d | 0a 00 00 17 4f 04 0d 0b |1- 2) ..|....O...|
|00002ef0| 00 47 6f 6f 64 2e 20 20 | 54 68 65 20 65 71 75 61 |.Good.  |The equa|
|00002f00| 74 69 6f 6e 20 6f 66 20 | 74 68 65 20 70 61 72 61 |tion of |the para|
|00002f10| 62 6f 6c 61 20 77 69 74 | 68 20 76 65 72 74 65 78 |bola wit|h vertex|
|00002f20| 20 28 32 2c 20 30 29 20 | 61 6e 64 20 70 61 73 73 | (2, 0) |and pass|
|00002f30| 69 6e 67 20 74 68 72 6f | 75 67 68 0d 0a 00 20 20 |ing thro|ugh...  |
|00002f40| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002f50| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002f60| 11 32 32 0d 0b 00 11 31 | 74 68 65 20 70 6f 69 6e |.22....1|the poin|
|00002f70| 74 20 28 30 2c 20 34 29 | 20 69 73 20 11 33 66 11 |t (0, 4)| is .3f.|
|00002f80| 31 28 11 33 78 11 31 29 | 20 3d 20 28 11 33 78 20 |1(.3x.1)| = (.3x |
|00002f90| 11 31 2d 20 32 29 20 2e | 0d 0a 00 00 17 4f 09 0d |.1- 2) .|.....O..|
|00002fa0| 0b 00 57 72 6f 6e 67 2e | 20 20 53 69 6e 63 65 20 |..Wrong.|  Since |
|00002fb0| 74 68 65 20 70 61 72 61 | 62 6f 6c 61 20 68 61 73 |the para|bola has|
|00002fc0| 20 61 20 76 65 72 74 65 | 78 20 61 74 20 28 11 33 | a verte|x at (.3|
|00002fd0| 68 11 31 2c 20 11 33 6b | 11 31 29 20 3d 20 28 32 |h.1, .3k|.1) = (2|
|00002fe0| 2c 20 30 29 2c 20 74 68 | 65 20 65 71 75 61 74 69 |, 0), th|e equati|
|00002ff0| 6f 6e 20 0d 0a 00 6d 75 | 73 74 20 68 61 76 65 20 |on ...mu|st have |
|00003000| 74 68 65 20 66 6f 6c 6c | 6f 77 69 6e 67 20 66 6f |the foll|owing fo|
|00003010| 72 6d 2e 12 38 0d 0a 00 | 20 20 20 20 20 20 20 20 |rm..8...|        |
|00003020| 20 20 20 20 20 20 20 20 | 20 20 11 33 68 20 20 20 |        |  .3h   |
|00003030| 20 20 6b 0d 0a 00 20 20 | 20 20 20 20 20 20 20 20 |  k...  |        |
|00003040| 20 20 20 20 20 20 20 20 | 11 34 21 20 20 20 20 20 |        |.4!     |
|00003050| 21 0d 0b 00 20 20 20 20 | 20 20 20 20 20 20 20 20 |!...    |        |
|00003060| 20 20 20 20 20 20 37 20 | 20 20 20 20 37 0d 0b 00 |      7 |    7...|
|00003070| 11 31 12 30 20 20 20 20 | 20 20 20 20 20 20 20 20 |.1.0    |        |
|00003080| 20 20 20 20 20 20 20 20 | 11 32 32 0d 0b 00 20 20 |        |.22...  |
|00003090| 20 20 20 11 33 66 11 31 | 28 11 33 78 11 31 29 20 |   .3f.1|(.3x.1) |
|000030a0| 3d 20 11 33 61 11 31 28 | 11 33 78 20 11 31 2d 20 |= .3a.1(|.3x .1- |
|000030b0| 32 29 20 20 2b 20 30 20 | 20 20 20 20 20 20 20 20 |2)  + 0 |        |
|000030c0| 20 11 32 12 31 53 74 61 | 6e 64 61 72 64 20 66 6f | .2.1Sta|ndard fo|
|000030d0| 72 6d 12 30 0d 0a 00 11 | 31 54 68 65 20 70 61 72 |rm.0....|1The par|
|000030e0| 61 62 6f 6c 61 20 70 61 | 73 73 65 73 20 74 68 72 |abola pa|sses thr|
|000030f0| 6f 75 67 68 20 74 68 65 | 20 70 6f 69 6e 74 20 28 |ough the| point (|
|00003100| 30 2c 20 34 29 2c 20 73 | 6f 20 69 74 20 66 6f 6c |0, 4), s|o it fol|
|00003110| 6c 6f 77 73 20 74 68 61 | 74 20 11 33 66 11 31 28 |lows tha|t .3f.1(|
|00003120| 30 29 20 3d 20 34 2e 0d | 0a 00 20 20 20 20 20 20 |0) = 4..|..      |
|00003130| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003140| 20 20 20 20 20 20 11 32 | 32 0d 0b 00 11 31 54 68 |      .2|2....1Th|
|00003150| 75 73 2c 20 77 65 20 6f | 62 74 61 69 6e 20 34 20 |us, we o|btain 4 |
|00003160| 3d 20 11 33 61 11 31 28 | 30 20 2d 20 32 29 20 20 |= .3a.1(|0 - 2)  |
|00003170| 20 20 20 20 11 34 35 35 | 36 20 20 20 20 20 11 33 |    .455|6     .3|
|00003180| 61 20 11 31 3d 20 31 2e | 0d 0a 00 20 20 20 20 20 |a .1= 1.|...     |
|00003190| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000031a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000031b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000031c0| 20 20 20 20 20 20 20 20 | 20 20 20 11 32 32 0d 0b |        |   .22..|
|000031d0| 00 11 31 54 68 69 73 20 | 69 6d 70 6c 69 65 73 20 |..1This |implies |
|000031e0| 74 68 61 74 20 74 68 65 | 20 65 71 75 61 74 69 6f |that the| equatio|
|000031f0| 6e 20 6f 66 20 74 68 65 | 20 70 61 72 61 62 6f 6c |n of the| parabol|
|00003200| 61 20 69 73 20 11 33 66 | 11 31 28 11 33 78 11 31 |a is .3f|.1(.3x.1|
|00003210| 29 20 3d 20 28 11 33 78 | 20 11 31 2d 20 32 29 20 |) = (.3x| .1- 2) |
|00003220| 2e 0d 0a 00 00 17 4f 09 | 0d 0b 00 57 72 6f 6e 67 |......O.|...Wrong|
|00003230| 2e 20 20 53 69 6e 63 65 | 20 74 68 65 20 70 61 72 |.  Since| the par|
|00003240| 61 62 6f 6c 61 20 68 61 | 73 20 61 20 76 65 72 74 |abola ha|s a vert|
|00003250| 65 78 20 61 74 20 28 11 | 33 68 11 31 2c 20 11 33 |ex at (.|3h.1, .3|
|00003260| 6b 11 31 29 20 3d 20 28 | 32 2c 20 30 29 2c 20 74 |k.1) = (|2, 0), t|
|00003270| 68 65 20 65 71 75 61 74 | 69 6f 6e 20 0d 0a 00 6d |he equat|ion ...m|
|00003280| 75 73 74 20 68 61 76 65 | 20 74 68 65 20 66 6f 6c |ust have| the fol|
|00003290| 6c 6f 77 69 6e 67 20 66 | 6f 72 6d 2e 12 38 0d 0a |lowing f|orm..8..|
|000032a0| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.       |        |
|000032b0| 20 20 20 11 33 68 20 20 | 20 20 20 6b 0d 0a 00 20 |   .3h  |   k... |
|000032c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000032d0| 20 11 34 21 20 20 20 20 | 20 21 0d 0b 00 20 20 20 | .4!    | !...   |
|000032e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 37 |        |       7|
|000032f0| 20 20 20 20 20 37 0d 0b | 00 11 31 12 30 20 20 20 |     7..|..1.0   |
|00003300| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003310| 20 11 32 32 0d 0b 00 20 | 20 20 20 20 11 33 66 11 | .22... |    .3f.|
|00003320| 31 28 11 33 78 11 31 29 | 20 3d 20 11 33 61 11 31 |1(.3x.1)| = .3a.1|
|00003330| 28 11 33 78 20 11 31 2d | 20 32 29 20 20 2b 20 30 |(.3x .1-| 2)  + 0|
|00003340| 20 20 20 20 20 20 20 20 | 20 20 11 32 12 31 53 74 |        |  .2.1St|
|00003350| 61 6e 64 61 72 64 20 66 | 6f 72 6d 12 30 0d 0a 00 |andard f|orm.0...|
|00003360| 11 31 54 68 65 20 70 61 | 72 61 62 6f 6c 61 20 70 |.1The pa|rabola p|
|00003370| 61 73 73 65 73 20 74 68 | 72 6f 75 67 68 20 74 68 |asses th|rough th|
|00003380| 65 20 70 6f 69 6e 74 20 | 28 30 2c 20 34 29 2c 20 |e point |(0, 4), |
|00003390| 73 6f 20 69 74 20 66 6f | 6c 6c 6f 77 73 20 74 68 |so it fo|llows th|
|000033a0| 61 74 20 11 33 66 11 31 | 28 30 29 20 3d 20 34 2e |at .3f.1|(0) = 4.|
|000033b0| 0d 0a 00 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |...     |        |
|000033c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 |        |       .|
|000033d0| 32 32 0d 0b 00 11 31 54 | 68 75 73 2c 20 77 65 20 |22....1T|hus, we |
|000033e0| 6f 62 74 61 69 6e 20 34 | 20 3d 20 11 33 61 11 31 |obtain 4| = .3a.1|
|000033f0| 28 30 20 2d 20 32 29 20 | 20 20 20 20 20 11 34 35 |(0 - 2) |     .45|
|00003400| 35 36 20 20 20 20 20 11 | 33 61 20 11 31 3d 20 31 |56     .|3a .1= 1|
|00003410| 2e 0d 0a 00 20 20 20 20 | 20 20 20 20 20 20 20 20 |....    |        |
|00003420| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003430| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003440| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003450| 20 20 20 20 11 32 32 0d | 0b 00 11 31 54 68 69 73 |    .22.|...1This|
|00003460| 20 69 6d 70 6c 69 65 73 | 20 74 68 61 74 20 74 68 | implies| that th|
|00003470| 65 20 65 71 75 61 74 69 | 6f 6e 20 6f 66 20 74 68 |e equati|on of th|
|00003480| 65 20 70 61 72 61 62 6f | 6c 61 20 69 73 20 11 33 |e parabo|la is .3|
|00003490| 66 11 31 28 11 33 78 11 | 31 29 20 3d 20 28 11 33 |f.1(.3x.|1) = (.3|
|000034a0| 78 20 11 31 2d 20 32 29 | 20 2e 0d 0a 00 53 65 63 |x .1- 2)| ....Sec|
|000034b0| 74 69 6f 6e 20 33 2e 31 | 20 20 51 75 61 64 72 61 |tion 3.1|  Quadra|
|000034c0| 74 69 63 20 46 75 6e 63 | 74 69 6f 6e 73 0d 0a 00 |tic Func|tions...|
|000034d0| 0d 0a 00 0d 0b 00 20 20 | 20 20 0e 78 33 2d 31 2d |......  |  .x3-1-|
|000034e0| 31 0e 54 75 74 6f 72 69 | 61 6c 20 45 78 65 72 63 |1.Tutori|al Exerc|
|000034f0| 69 73 65 20 20 31 0f 20 | 20 20 20 0e 78 33 2d 31 |ise  1. |   .x3-1|
|00003500| 2d 32 0e 54 75 74 6f 72 | 69 61 6c 20 45 78 65 72 |-2.Tutor|ial Exer|
|00003510| 63 69 73 65 20 20 32 0f | 0d 0a 00 0d 0b 00 20 20 |cise  2.|......  |
|00003520| 20 20 0e 78 33 2d 31 2d | 33 0e 54 75 74 6f 72 69 |  .x3-1-|3.Tutori|
|00003530| 61 6c 20 45 78 65 72 63 | 69 73 65 20 20 33 0f 0d |al Exerc|ise  3..|
|00003540| 0a 00 0d 0b 00 20 20 20 | 20 0e 78 33 2d 31 2d 34 |.....   | .x3-1-4|
|00003550| 0e 54 75 74 6f 72 69 61 | 6c 20 45 78 65 72 63 69 |.Tutoria|l Exerci|
|00003560| 73 65 20 20 34 0f 0d 0a | 00 0d 0b 00 20 20 20 20 |se  4...|....    |
|00003570| 0e 78 33 2d 31 2d 35 0e | 54 75 74 6f 72 69 61 6c |.x3-1-5.|Tutorial|
|00003580| 20 45 78 65 72 63 69 73 | 65 20 20 35 0f 0d 0a 00 | Exercis|e  5....|
|00003590| 0d 0b 00 20 20 20 20 0e | 78 33 2d 31 2d 36 0e 54 |...    .|x3-1-6.T|
|000035a0| 75 74 6f 72 69 61 6c 20 | 45 78 65 72 63 69 73 65 |utorial |Exercise|
|000035b0| 20 20 36 0f 20 20 20 20 | 0e 78 33 2d 31 2d 37 0e |  6.    |.x3-1-7.|
|000035c0| 54 75 74 6f 72 69 61 6c | 20 45 78 65 72 63 69 73 |Tutorial| Exercis|
|000035d0| 65 20 20 37 0f 20 20 20 | 20 0e 78 33 2d 31 2d 38 |e  7.   | .x3-1-8|
|000035e0| 0e 54 75 74 6f 72 69 61 | 6c 20 45 78 65 72 63 69 |.Tutoria|l Exerci|
|000035f0| 73 65 20 20 38 0f 0d 0a | 00 53 65 63 74 69 6f 6e |se  8...|.Section|
|00003600| 20 33 2e 31 20 20 51 75 | 61 64 72 61 74 69 63 20 | 3.1  Qu|adratic |
|00003610| 46 75 6e 63 74 69 6f 6e | 73 0d 0b 00 20 31 2e 20 |Function|s... 1. |
|00003620| 20 46 69 6e 64 20 61 6e | 20 65 71 75 61 74 69 6f | Find an| equatio|
|00003630| 6e 20 66 6f 72 20 74 68 | 65 20 70 61 72 61 62 6f |n for th|e parabo|
|00003640| 6c 61 20 20 20 20 14 6a | 34 2d 31 2d 37 2e 6d 14 |la    .j|4-1-7.m.|
|00003650| 34 35 14 31 14 32 30 14 | 37 14 0d 0a 00 20 20 20 |45.1.20.|7....   |
|00003660| 20 20 73 68 6f 77 6e 20 | 61 74 20 74 68 65 20 72 |  shown |at the r|
|00003670| 69 67 68 74 2e 0d 0a 00 | 0d 0a 00 20 20 20 20 20 |ight....|...     |
|00003680| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003690| 20 20 20 11 32 32 0d 0b | 00 20 20 20 20 20 11 31 |   .22..|.     .1|
|000036a0| 0e 61 34 2d 31 2d 37 61 | 0e 28 61 29 0f 20 11 33 |.a4-1-7a|.(a). .3|
|000036b0| 66 11 31 28 11 33 78 11 | 31 29 20 3d 20 2d 28 11 |f.1(.3x.|1) = -(.|
|000036c0| 33 78 20 11 31 2d 20 32 | 29 0d 0a 00 20 20 20 20 |3x .1- 2|)...    |
|000036d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000036e0| 20 20 20 11 32 32 0d 0b | 00 20 20 20 20 20 11 31 |   .22..|.     .1|
|000036f0| 0e 61 34 2d 31 2d 37 62 | 0e 28 62 29 0f 20 11 33 |.a4-1-7b|.(b). .3|
|00003700| 66 11 31 28 11 33 78 11 | 31 29 20 3d 20 28 11 33 |f.1(.3x.|1) = (.3|
|00003710| 78 20 11 31 2d 20 32 29 | 0d 0a 00 20 20 20 20 20 |x .1- 2)|...     |
|00003720| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003730| 20 20 11 32 32 0d 0b 00 | 20 20 20 20 20 11 31 0e |  .22...|     .1.|
|00003740| 61 34 2d 31 2d 37 63 0e | 28 63 29 0f 20 11 33 66 |a4-1-7c.|(c). .3f|
|00003750| 11 31 28 11 33 78 11 31 | 29 20 3d 20 28 11 33 78 |.1(.3x.1|) = (.3x|
|00003760| 20 11 31 2d 20 34 29 0d | 0a 00 20 20 20 20 20 20 | .1- 4).|..      |
|00003770| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003780| 20 11 32 32 0d 0b 00 20 | 20 20 20 20 11 31 0e 61 | .22... |    .1.a|
|00003790| 34 2d 31 2d 37 64 0e 28 | 64 29 0f 20 11 33 66 11 |4-1-7d.(|d). .3f.|
|000037a0| 31 28 11 33 78 11 31 29 | 20 3d 20 28 11 33 78 20 |1(.3x.1)| = (.3x |
|000037b0| 11 31 2b 20 32 29 0d 0a | 00 0d 0a 00 59 6f 75 20 |.1+ 2)..|....You |
|000037c0| 6d 61 79 20 77 61 6e 74 | 20 74 6f 20 72 65 76 69 |may want| to revi|
|000037d0| 65 77 20 10 33 2d 31 2d | 32 0e 65 33 2d 31 2d 31 |ew .3-1-|2.e3-1-1|
|000037e0| 0e 47 75 69 64 65 64 20 | 45 78 61 6d 70 6c 65 20 |.Guided |Example |
|000037f0| 31 2e 0f 0d 0a 00 53 65 | 63 74 69 6f 6e 20 33 2e |1.....Se|ction 3.|
|00003800| 31 20 20 51 75 61 64 72 | 61 74 69 63 20 46 75 6e |1  Quadr|atic Fun|
|00003810| 63 74 69 6f 6e 73 0d 0b | 00 20 32 2e 20 20 46 69 |ctions..|. 2.  Fi|
|00003820| 6e 64 20 61 6e 20 65 71 | 75 61 74 69 6f 6e 20 66 |nd an eq|uation f|
|00003830| 6f 72 20 74 68 65 20 70 | 61 72 61 62 6f 6c 61 20 |or the p|arabola |
|00003840| 20 20 20 20 14 6a 34 2d | 31 2d 31 31 2e 6d 14 34 |    .j4-|1-11.m.4|
|00003850| 35 14 31 14 32 30 14 37 | 14 0d 0a 00 20 20 20 20 |5.1.20.7|....    |
|00003860| 20 73 68 6f 77 6e 20 61 | 74 20 74 68 65 20 72 69 | shown a|t the ri|
|00003870| 67 68 74 2e 0d 0a 00 0d | 0b 00 20 20 20 20 20 20 |ght.....|..      |
|00003880| 20 20 20 20 20 20 20 20 | 20 20 20 20 32 20 20 20 |        |    2   |
|00003890| 20 20 20 20 11 32 32 0d | 0b 00 20 20 20 20 20 11 |    .22.|..     .|
|000038a0| 31 0e 61 34 2d 31 2d 31 | 31 61 0e 28 61 29 0f 20 |1.a4-1-1|1a.(a). |
|000038b0| 11 33 66 11 31 28 11 33 | 78 11 31 29 20 3d 20 2d |.3f.1(.3|x.1) = -|
|000038c0| 11 34 32 32 11 31 28 11 | 33 78 20 11 31 2d 20 33 |.422.1(.|3x .1- 3|
|000038d0| 29 20 20 2b 20 33 0d 0b | 00 20 20 20 20 20 20 20 |)  + 3..|.       |
|000038e0| 20 20 20 20 20 20 20 20 | 20 20 32 35 0d 0a 00 0d |        |  25....|
|000038f0| 0b 00 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |..      |        |
|00003900| 20 20 31 0d 0b 00 20 20 | 20 20 20 0e 61 34 2d 31 |  1...  |   .a4-1|
|00003910| 2d 31 31 62 0e 28 62 29 | 0f 20 11 33 66 11 31 28 |-11b.(b)|. .3f.1(|
|00003920| 11 33 78 11 31 29 20 3d | 20 11 34 32 11 31 28 11 |.3x.1) =| .42.1(.|
|00003930| 33 78 20 11 31 2b 20 33 | 29 20 2d 20 33 0d 0b 00 |3x .1+ 3|) - 3...|
|00003940| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003950| 34 0d 0a 00 0d 0b 00 20 | 20 20 20 20 20 20 20 20 |4...... |        |
|00003960| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003970| 11 32 32 0d 0b 00 20 20 | 20 20 20 11 31 0e 61 34 |.22...  |   .1.a4|
|00003980| 2d 31 2d 31 31 63 0e 28 | 63 29 0f 20 11 33 66 11 |-1-11c.(|c). .3f.|
|00003990| 31 28 11 33 78 11 31 29 | 20 3d 20 2d 32 28 11 33 |1(.3x.1)| = -2(.3|
|000039a0| 78 20 11 31 2b 20 33 29 | 20 20 2b 20 33 0d 0a 00 |x .1+ 3)|  + 3...|
|000039b0| 0d 0a 00 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |...     |        |
|000039c0| 20 20 20 20 20 20 20 20 | 20 20 11 32 32 0d 0b 00 |        |  .22...|
|000039d0| 20 20 20 20 20 11 31 0e | 61 34 2d 31 2d 31 31 64 |     .1.|a4-1-11d|
|000039e0| 0e 28 64 29 0f 20 11 33 | 66 11 31 28 11 33 78 11 |.(d). .3|f.1(.3x.|
|000039f0| 31 29 20 3d 20 28 11 33 | 78 20 11 31 2b 20 33 29 |1) = (.3|x .1+ 3)|
|00003a00| 20 20 2b 20 33 0d 0a 00 | 0d 0a 00 59 6f 75 20 6d |  + 3...|...You m|
|00003a10| 61 79 20 77 61 6e 74 20 | 74 6f 20 72 65 76 69 65 |ay want |to revie|
|00003a20| 77 20 10 33 2d 31 2d 32 | 0e 65 33 2d 31 2d 31 0e |w .3-1-2|.e3-1-1.|
|00003a30| 47 75 69 64 65 64 20 45 | 78 61 6d 70 6c 65 20 31 |Guided E|xample 1|
|00003a40| 2e 0f 0d 0a 00 53 65 63 | 74 69 6f 6e 20 33 2e 31 |.....Sec|tion 3.1|
|00003a50| 20 20 51 75 61 64 72 61 | 74 69 63 20 46 75 6e 63 |  Quadra|tic Func|
|00003a60| 74 69 6f 6e 73 0d 0b 00 | 20 33 2e 20 20 46 69 6e |tions...| 3.  Fin|
|00003a70| 64 20 74 68 65 20 71 75 | 61 64 72 61 74 69 63 20 |d the qu|adratic |
|00003a80| 66 75 6e 63 74 69 6f 6e | 20 74 68 61 74 20 68 61 |function| that ha|
|00003a90| 73 20 61 20 76 65 72 74 | 65 78 20 61 74 20 28 2d |s a vert|ex at (-|
|00003aa0| 31 2c 20 33 29 20 61 6e | 64 20 77 68 6f 73 65 20 |1, 3) an|d whose |
|00003ab0| 67 72 61 70 68 0d 0a 00 | 20 20 20 20 20 70 61 73 |graph...|     pas|
|00003ac0| 73 65 73 20 74 68 72 6f | 75 67 68 20 74 68 65 20 |ses thro|ugh the |
|00003ad0| 70 6f 69 6e 74 20 28 32 | 2c 20 31 29 2e 0d 0a 00 |point (2|, 1)....|
|00003ae0| 0d 0a 00 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |...     |        |
|00003af0| 20 20 20 20 32 20 20 20 | 20 20 20 20 11 32 32 20 |    2   |    .22 |
|00003b00| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003b10| 20 20 20 20 20 20 11 31 | 34 20 20 20 20 20 20 20 |      .1|4       |
|00003b20| 11 32 32 0d 0b 00 20 20 | 20 20 20 11 31 0e 61 34 |.22...  |   .1.a4|
|00003b30| 2d 31 2d 33 33 63 0e 28 | 61 29 0f 20 11 33 66 11 |-1-33c.(|a). .3f.|
|00003b40| 31 28 11 33 78 11 31 29 | 20 3d 20 2d 11 34 32 11 |1(.3x.1)| = -.42.|
|00003b50| 31 28 11 33 78 20 11 31 | 2b 20 31 29 20 20 2b 20 |1(.3x .1|+ 1)  + |
|00003b60| 33 20 20 20 20 20 20 20 | 20 0e 61 34 2d 31 2d 33 |3       | .a4-1-3|
|00003b70| 33 62 0e 28 62 29 0f 20 | 11 33 66 11 31 28 11 33 |3b.(b). |.3f.1(.3|
|00003b80| 78 11 31 29 20 3d 20 11 | 34 32 11 31 28 11 33 78 |x.1) = .|42.1(.3x|
|00003b90| 20 11 31 2b 20 31 29 20 | 20 2b 20 33 0d 0b 00 20 | .1+ 1) | + 3... |
|00003ba0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003bb0| 39 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |9       |        |
|00003bc0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003bd0| 39 0d 0a 00 0d 0b 00 20 | 20 20 20 20 20 20 20 20 |9...... |        |
|00003be0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003bf0| 11 32 32 0d 0b 00 20 20 | 20 20 20 11 31 0e 61 34 |.22...  |   .1.a4|
|00003c00| 2d 31 2d 33 33 61 0e 28 | 63 29 0f 20 11 33 66 11 |-1-33a.(|c). .3f.|
|00003c10| 31 28 11 33 78 11 31 29 | 20 3d 20 2d 32 28 11 33 |1(.3x.1)| = -2(.3|
|00003c20| 78 20 11 31 2d 20 31 29 | 20 20 2b 20 33 20 20 20 |x .1- 1)|  + 3   |
|00003c30| 20 20 20 20 20 0e 61 34 | 2d 31 2d 33 33 64 0e 28 |     .a4|-1-33d.(|
|00003c40| 64 29 0f 20 4e 6f 74 20 | 65 6e 6f 75 67 68 20 69 |d). Not |enough i|
|00003c50| 6e 66 6f 72 6d 61 74 69 | 6f 6e 0d 0a 00 0d 0a 00 |nformati|on......|
|00003c60| 59 6f 75 20 6d 61 79 20 | 77 61 6e 74 20 74 6f 20 |You may |want to |
|00003c70| 72 65 76 69 65 77 20 10 | 33 2d 31 2d 32 0e 65 33 |review .|3-1-2.e3|
|00003c80| 2d 31 2d 32 0e 47 75 69 | 64 65 64 20 45 78 61 6d |-1-2.Gui|ded Exam|
|00003c90| 70 6c 65 20 32 2e 0f 0d | 0a 00 53 65 63 74 69 6f |ple 2...|..Sectio|
|00003ca0| 6e 20 33 2e 31 20 20 51 | 75 61 64 72 61 74 69 63 |n 3.1  Q|uadratic|
|00003cb0| 20 46 75 6e 63 74 69 6f | 6e 73 0d 0b 00 20 34 2e | Functio|ns... 4.|
|00003cc0| 20 20 41 20 72 61 6e 63 | 68 65 72 20 68 61 73 20 |  A ranc|her has |
|00003cd0| 32 30 30 20 66 65 65 74 | 20 6f 66 20 66 65 6e 63 |200 feet| of fenc|
|00003ce0| 69 6e 67 20 74 6f 20 20 | 20 20 20 14 6a 34 2d 31 |ing to  |   .j4-1|
|00003cf0| 2d 34 33 2e 6d 14 34 38 | 14 31 14 32 30 14 37 14 |-43.m.48|.1.20.7.|
|00003d00| 0d 0a 00 20 20 20 20 20 | 65 6e 63 6c 6f 73 65 20 |...     |enclose |
|00003d10| 74 77 6f 20 61 64 6a 61 | 63 65 6e 74 20 72 65 63 |two adja|cent rec|
|00003d20| 74 61 6e 67 75 6c 61 72 | 20 0d 0a 00 20 20 20 20 |tangular| ...    |
|00003d30| 20 63 6f 72 72 61 6c 73 | 20 28 73 65 65 20 66 69 | corrals| (see fi|
|00003d40| 67 75 72 65 29 2e 20 20 | 57 68 61 74 20 64 69 6d |gure).  |What dim|
|00003d50| 65 6e 73 69 6f 6e 73 0d | 0a 00 20 20 20 20 20 70 |ensions.|..     p|
|00003d60| 72 6f 64 75 63 65 20 61 | 20 6d 61 78 69 6d 75 6d |roduce a| maximum|
|00003d70| 20 65 6e 63 6c 6f 73 65 | 64 20 61 72 65 61 3f 0d | enclose|d area?.|
|00003d80| 0a 00 0d 0a 00 20 20 20 | 20 20 0e 61 34 2d 31 2d |.....   |  .a4-1-|
|00003d90| 34 33 61 0e 28 61 29 0f | 20 11 33 78 20 11 31 3d |43a.(a).| .3x .1=|
|00003da0| 20 32 35 20 66 65 65 74 | 2c 20 11 33 79 20 11 31 | 25 feet|, .3y .1|
|00003db0| 3d 20 32 35 20 66 65 65 | 74 0d 0a 00 0d 0a 00 0d |= 25 fee|t.......|
|00003dc0| 0b 00 20 20 20 20 20 0e | 61 34 2d 31 2d 34 33 62 |..     .|a4-1-43b|
|00003dd0| 0e 28 62 29 0f 20 11 33 | 78 20 11 31 3d 20 35 30 |.(b). .3|x .1= 50|
|00003de0| 20 66 65 65 74 2c 20 11 | 33 79 20 11 31 3d 20 35 | feet, .|3y .1= 5|
|00003df0| 30 20 66 65 65 74 0d 0a | 00 0d 0a 00 20 20 20 20 |0 feet..|....    |
|00003e00| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003e10| 20 20 20 20 20 20 20 20 | 31 0d 0b 00 20 20 20 20 |        |1...    |
|00003e20| 20 0e 61 34 2d 31 2d 34 | 33 63 0e 28 63 29 0f 20 | .a4-1-4|3c.(c). |
|00003e30| 11 33 78 20 11 31 3d 20 | 32 35 20 66 65 65 74 2c |.3x .1= |25 feet,|
|00003e40| 20 11 33 79 20 11 31 3d | 20 33 33 11 34 32 20 11 | .3y .1=| 33.42 .|
|00003e50| 31 66 65 65 74 0d 0b 00 | 20 20 20 20 20 20 20 20 |1feet...|        |
|00003e60| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003e70| 20 20 20 20 33 0d 0a 00 | 0d 0b 00 20 20 20 20 20 |    3...|...     |
|00003e80| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003e90| 20 20 20 20 20 20 20 31 | 0d 0b 00 20 20 20 20 20 |       1|...     |
|00003ea0| 0e 61 34 2d 31 2d 34 33 | 64 0e 28 64 29 0f 20 11 |.a4-1-43|d.(d). .|
|00003eb0| 33 78 20 11 31 3d 20 35 | 30 20 66 65 65 74 2c 20 |3x .1= 5|0 feet, |
|00003ec0| 11 33 79 20 11 31 3d 20 | 33 33 11 34 32 20 11 31 |.3y .1= |33.42 .1|
|00003ed0| 66 65 65 74 0d 0b 00 20 | 20 20 20 20 20 20 20 20 |feet... |        |
|00003ee0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003ef0| 20 20 20 33 0d 0a 00 0d | 0a 00 59 6f 75 20 6d 61 |   3....|..You ma|
|00003f00| 79 20 77 61 6e 74 20 74 | 6f 20 72 65 76 69 65 77 |y want t|o review|
|00003f10| 20 10 33 2d 31 2d 32 0e | 65 33 2d 31 2d 33 0e 47 | .3-1-2.|e3-1-3.G|
|00003f20| 75 69 64 65 64 20 45 78 | 61 6d 70 6c 65 20 33 2e |uided Ex|ample 3.|
|00003f30| 0f 0d 0a 00 53 65 63 74 | 69 6f 6e 20 33 2e 31 20 |....Sect|ion 3.1 |
|00003f40| 20 51 75 61 64 72 61 74 | 69 63 20 46 75 6e 63 74 | Quadrat|ic Funct|
|00003f50| 69 6f 6e 73 20 20 20 20 | 20 20 20 20 20 20 20 20 |ions    |        |
|00003f60| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003f70| 20 20 20 20 20 20 11 32 | 32 0d 0b 00 20 11 31 35 |      .2|2... .15|
|00003f80| 2e 20 20 53 6b 65 74 63 | 68 20 74 68 65 20 67 72 |.  Sketc|h the gr|
|00003f90| 61 70 68 20 6f 66 20 11 | 33 68 11 31 28 11 33 78 |aph of .|3h.1(.3x|
|00003fa0| 11 31 29 20 3d 20 34 11 | 33 78 20 20 11 31 2d 20 |.1) = 4.|3x  .1- |
|00003fb0| 34 11 33 78 20 11 31 2b | 20 32 31 2e 20 20 49 64 |4.3x .1+| 21.  Id|
|00003fc0| 65 6e 74 69 66 79 20 74 | 68 65 20 76 65 72 74 65 |entify t|he verte|
|00003fd0| 78 20 61 6e 64 20 0d 0a | 00 20 20 20 20 20 69 6e |x and ..|.     in|
|00003fe0| 74 65 72 63 65 70 74 73 | 2e 0d 0a 00 0d 0a 00 20 |tercepts|....... |
|00003ff0| 20 20 20 20 0e 61 34 2d | 31 2d 32 37 61 0e 28 61 |    .a4-|1-27a.(a|
|00004000| 29 0f 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |).      |        |
|00004010| 20 20 20 20 20 20 0e 61 | 34 2d 31 2d 32 37 62 0e |      .a|4-1-27b.|
|00004020| 28 62 29 0f 20 20 20 20 | 20 20 20 20 20 20 20 20 |(b).    |        |
|00004030| 20 20 20 20 20 20 20 0e | 61 34 2d 31 2d 32 37 63 |       .|a4-1-27c|
|00004040| 0e 28 63 29 0f 20 0d 0a | 00 14 6a 34 2d 31 2d 32 |.(c). ..|..j4-1-2|
|00004050| 37 61 2e 6d 14 39 14 37 | 14 32 30 14 37 14 20 20 |7a.m.9.7|.20.7.  |
|00004060| 14 6a 34 2d 31 2d 32 37 | 62 2e 6d 14 33 31 14 37 |.j4-1-27|b.m.31.7|
|00004070| 14 32 30 14 37 14 20 20 | 14 6a 34 2d 31 2d 32 37 |.20.7.  |.j4-1-27|
|00004080| 63 2e 6d 14 35 33 14 37 | 14 32 30 14 37 14 0d 0a |c.m.53.7|.20.7...|
|00004090| 00 0d 0a 00 0d 0a 00 0d | 0a 00 0d 0a 00 0d 0a 00 |........|........|
|000040a0| 0d 0b 00 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |...     |        |
|000040b0| 20 20 20 20 20 31 20 20 | 20 20 20 20 20 20 20 20 |     1  |        |
|000040c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 31 20 20 20 |        |    1   |
|000040d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000040e0| 20 31 20 20 38 33 0d 0b | 00 20 20 20 20 20 20 20 | 1  83..|.       |
|000040f0| 20 20 56 65 72 74 65 78 | 3a 20 28 11 34 32 11 31 |  Vertex|: (.42.1|
|00004100| 2c 20 32 30 29 20 20 20 | 20 20 20 20 56 65 72 74 |, 20)   |    Vert|
|00004110| 65 78 3a 20 28 2d 11 34 | 32 11 31 2c 20 32 30 29 |ex: (-.4|2.1, 20)|
|00004120| 20 20 20 20 20 20 56 65 | 72 74 65 78 3a 20 28 11 |      Ve|rtex: (.|
|00004130| 34 32 11 31 2c 20 11 34 | 32 32 11 31 29 0d 0b 00 |42.1, .4|22.1)...|
|00004140| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00004150| 20 20 32 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |  2     |        |
|00004160| 20 20 20 20 20 20 20 20 | 20 32 20 20 20 20 20 20 |        | 2      |
|00004170| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 34 20 |        |      4 |
|00004180| 20 20 34 0d 0a 00 0d 0b | 00 20 20 20 20 20 20 20 |  4.....|.       |
|00004190| 20 20 49 6e 74 65 72 63 | 65 70 74 3a 20 28 30 2c |  Interc|ept: (0,|
|000041a0| 20 32 31 29 20 20 20 20 | 49 6e 74 65 72 63 65 70 | 21)    |Intercep|
|000041b0| 74 3a 20 28 30 2c 20 32 | 30 29 20 20 20 20 49 6e |t: (0, 2|0)    In|
|000041c0| 74 65 72 63 65 70 74 3a | 20 28 30 2c 20 32 31 29 |tercept:| (0, 21)|
|000041d0| 0d 0a 00 0d 0a 00 0d 0b | 00 20 20 20 20 20 0e 61 |........|.     .a|
|000041e0| 34 2d 31 2d 32 37 64 0e | 28 64 29 0f 20 4e 6f 6e |4-1-27d.|(d). Non|
|000041f0| 65 20 6f 66 20 74 68 65 | 73 65 0d 0a 00 0d 0a 00 |e of the|se......|
|00004200| 59 6f 75 20 6d 61 79 20 | 77 61 6e 74 20 74 6f 20 |You may |want to |
|00004210| 72 65 76 69 65 77 20 10 | 33 2d 31 2d 32 0e 69 33 |review .|3-1-2.i3|
|00004220| 2d 31 2d 34 0e 49 6e 74 | 65 67 72 61 74 65 64 20 |-1-4.Int|egrated |
|00004230| 45 78 61 6d 70 6c 65 20 | 34 2e 0f 0d 0a 00 53 65 |Example |4.....Se|
|00004240| 63 74 69 6f 6e 20 33 2e | 31 20 20 51 75 61 64 72 |ction 3.|1  Quadr|
|00004250| 61 74 69 63 20 46 75 6e | 63 74 69 6f 6e 73 20 20 |atic Fun|ctions  |
|00004260| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00004270| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00004280| 20 20 20 20 20 11 32 32 | 0d 0b 00 20 11 31 36 2e |     .22|... .16.|
|00004290| 20 20 53 6b 65 74 63 68 | 20 74 68 65 20 67 72 61 |  Sketch| the gra|
|000042a0| 70 68 20 6f 66 20 11 33 | 66 11 31 28 11 33 78 11 |ph of .3|f.1(.3x.|
|000042b0| 31 29 20 3d 20 28 11 33 | 78 20 11 31 2b 20 35 29 |1) = (.3|x .1+ 5)|
|000042c0| 20 20 2d 20 36 2e 20 20 | 49 64 65 6e 74 69 66 79 |  - 6.  |Identify|
|000042d0| 20 74 68 65 20 76 65 72 | 74 65 78 20 61 6e 64 20 | the ver|tex and |
|000042e0| 0d 0a 00 20 20 20 20 20 | 69 6e 74 65 72 63 65 70 |...     |intercep|
|000042f0| 74 73 2e 0d 0a 00 0d 0a | 00 20 20 20 20 20 0e 61 |ts......|.     .a|
|00004300| 34 2d 31 2d 31 37 61 0e | 28 61 29 0f 20 20 20 20 |4-1-17a.|(a).    |
|00004310| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00004320| 0e 61 34 2d 31 2d 31 37 | 62 0e 28 62 29 0f 20 20 |.a4-1-17|b.(b).  |
|00004330| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00004340| 20 0e 61 34 2d 31 2d 31 | 37 63 0e 28 63 29 0f 20 | .a4-1-1|7c.(c). |
|00004350| 0d 0a 00 14 6a 34 2d 31 | 2d 31 37 61 2e 6d 14 39 |....j4-1|-17a.m.9|
|00004360| 14 37 14 32 30 14 37 14 | 20 20 14 6a 34 2d 31 2d |.7.20.7.|  .j4-1-|
|00004370| 31 37 62 2e 6d 14 33 31 | 14 37 14 32 30 14 37 14 |17b.m.31|.7.20.7.|
|00004380| 20 20 14 6a 34 2d 31 2d | 31 37 63 2e 6d 14 35 33 |  .j4-1-|17c.m.53|
|00004390| 14 37 14 32 30 14 37 14 | 0d 0a 00 0d 0a 00 0d 0a |.7.20.7.|........|
|000043a0| 00 0d 0a 00 0d 0a 00 0d | 0a 00 0d 0b 00 20 20 20 |........|.....   |
|000043b0| 20 20 20 20 20 20 56 65 | 72 74 65 78 3a 20 28 2d |      Ve|rtex: (-|
|000043c0| 35 2c 20 2d 36 29 20 20 | 20 20 20 20 56 65 72 74 |5, -6)  |    Vert|
|000043d0| 65 78 3a 20 28 35 2c 20 | 36 29 20 20 20 20 20 20 |ex: (5, |6)      |
|000043e0| 20 20 56 65 72 74 65 78 | 3a 20 28 35 2c 20 2d 36 |  Vertex|: (5, -6|
|000043f0| 29 0d 0a 00 20 20 20 20 | 20 20 20 20 20 49 6e 74 |)...    |     Int|
|00004400| 65 72 63 65 70 74 73 3a | 20 28 30 2c 20 31 39 29 |ercepts:| (0, 19)|
|00004410| 20 20 20 49 6e 74 65 72 | 63 65 70 74 3a 20 28 30 |   Inter|cept: (0|
|00004420| 2c 20 33 31 29 20 20 20 | 20 49 6e 74 65 72 63 65 |, 31)   | Interce|
|00004430| 70 74 73 3a 20 28 30 2c | 20 31 39 29 0d 0a 00 20 |pts: (0,| 19)... |
|00004440| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00004450| 20 20 20 20 20 11 34 44 | 32 20 20 20 20 20 20 20 |     .4D|2       |
|00004460| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00004470| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00004480| 20 20 20 44 32 0d 0b 00 | 20 20 20 20 20 20 20 20 |   D2...|        |
|00004490| 20 20 20 20 20 20 20 11 | 31 28 2d 35 20 11 34 2b |       .|1(-5 .4+|
|000044a0| 20 53 20 11 31 36 2c 20 | 30 29 20 20 20 20 20 20 | S .16, |0)      |
|000044b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000044c0| 20 20 20 20 20 20 20 20 | 20 20 28 35 20 11 34 2b |        |  (5 .4+|
|000044d0| 20 53 20 11 31 36 2c 20 | 30 29 0d 0a 00 0d 0a 00 | S .16, |0)......|
|000044e0| 20 20 20 20 20 0e 61 34 | 2d 31 2d 31 37 64 0e 28 |     .a4|-1-17d.(|
|000044f0| 64 29 0f 20 4e 6f 6e 65 | 20 6f 66 20 74 68 65 73 |d). None| of thes|
|00004500| 65 0d 0a 00 0d 0a 00 59 | 6f 75 20 6d 61 79 20 77 |e......Y|ou may w|
|00004510| 61 6e 74 20 74 6f 20 72 | 65 76 69 65 77 20 10 33 |ant to r|eview .3|
|00004520| 2d 31 2d 32 0e 69 33 2d | 31 2d 31 0e 49 6e 74 65 |-1-2.i3-|1-1.Inte|
|00004530| 67 72 61 74 65 64 20 45 | 78 61 6d 70 6c 65 20 31 |grated E|xample 1|
|00004540| 2e 0f 0d 0a 00 53 65 63 | 74 69 6f 6e 20 33 2e 31 |.....Sec|tion 3.1|
|00004550| 20 20 51 75 61 64 72 61 | 74 69 63 20 46 75 6e 63 |  Quadra|tic Func|
|00004560| 74 69 6f 6e 73 20 20 20 | 20 20 20 20 20 20 20 20 |tions   |        |
|00004570| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00004580| 20 20 20 20 20 20 11 32 | 32 0d 0b 00 20 11 31 37 |      .2|2... .17|
|00004590| 2e 20 20 53 6b 65 74 63 | 68 20 74 68 65 20 67 72 |.  Sketc|h the gr|
|000045a0| 61 70 68 20 6f 66 20 11 | 33 68 11 31 28 11 33 78 |aph of .|3h.1(.3x|
|000045b0| 11 31 29 20 3d 20 11 33 | 78 20 20 11 31 2d 20 38 |.1) = .3|x  .1- 8|
|000045c0| 11 33 78 20 11 31 2b 20 | 31 36 2e 20 20 49 64 65 |.3x .1+ |16.  Ide|
|000045d0| 6e 74 69 66 79 20 74 68 | 65 20 76 65 72 74 65 78 |ntify th|e vertex|
|000045e0| 20 61 6e 64 20 0d 0a 00 | 20 20 20 20 20 69 6e 74 | and ...|     int|
|000045f0| 65 72 63 65 70 74 73 2e | 0d 0a 00 0d 0a 00 20 20 |ercepts.|......  |
|00004600| 20 20 20 0e 61 34 2d 31 | 2d 31 39 61 0e 28 61 29 |   .a4-1|-19a.(a)|
|00004610| 0f 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.       |        |
|00004620| 20 20 20 20 20 0e 61 34 | 2d 31 2d 31 39 62 0e 28 |     .a4|-1-19b.(|
|00004630| 62 29 0f 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |b).     |        |
|00004640| 20 20 20 20 20 20 0e 61 | 34 2d 31 2d 31 39 63 0e |      .a|4-1-19c.|
|00004650| 28 63 29 0f 20 0d 0a 00 | 14 6a 34 2d 31 2d 31 39 |(c). ...|.j4-1-19|
|00004660| 61 2e 6d 14 39 14 37 14 | 32 30 14 37 14 20 20 14 |a.m.9.7.|20.7.  .|
|00004670| 6a 34 2d 31 2d 31 39 62 | 2e 6d 14 33 31 14 37 14 |j4-1-19b|.m.31.7.|
|00004680| 32 30 14 37 14 20 20 14 | 6a 34 2d 31 2d 31 39 63 |20.7.  .|j4-1-19c|
|00004690| 2e 6d 14 35 33 14 37 14 | 32 30 14 37 14 0d 0a 00 |.m.53.7.|20.7....|
|000046a0| 0d 0a 00 0d 0a 00 0d 0a | 00 0d 0a 00 0d 0a 00 0d |........|........|
|000046b0| 0b 00 20 20 20 20 20 20 | 20 20 20 56 65 72 74 65 |..      |   Verte|
|000046c0| 78 3a 20 28 2d 34 2c 20 | 30 29 20 20 20 20 20 20 |x: (-4, |0)      |
|000046d0| 20 56 65 72 74 65 78 3a | 20 28 34 2c 20 30 29 20 | Vertex:| (4, 0) |
|000046e0| 20 20 20 20 20 20 20 56 | 65 72 74 65 78 3a 20 28 |       V|ertex: (|
|000046f0| 34 2c 20 30 29 0d 0a 00 | 20 20 20 20 20 20 20 20 |4, 0)...|        |
|00004700| 20 49 6e 74 65 72 63 65 | 70 74 73 3a 20 28 2d 34 | Interce|pts: (-4|
|00004710| 2c 20 30 29 20 20 20 49 | 6e 74 65 72 63 65 70 74 |, 0)   I|ntercept|
|00004720| 73 3a 20 28 34 2c 20 30 | 29 20 20 20 20 49 6e 74 |s: (4, 0|)    Int|
|00004730| 65 72 63 65 70 74 73 3a | 20 28 34 2c 20 30 29 0d |ercepts:| (4, 0).|
|00004740| 0a 00 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |..      |        |
|00004750| 20 20 20 20 20 20 20 28 | 30 2c 20 31 36 29 20 20 |       (|0, 16)  |
|00004760| 20 20 20 20 20 20 20 20 | 20 20 20 28 30 2c 20 2d |        |   (0, -|
|00004770| 31 36 29 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |16)     |        |
|00004780| 20 20 28 30 2c 20 31 36 | 29 0d 0a 00 0d 0a 00 20 |  (0, 16|)...... |
|00004790| 20 20 20 20 0e 61 34 2d | 31 2d 31 39 64 0e 28 64 |    .a4-|1-19d.(d|
|000047a0| 29 0f 20 4e 6f 6e 65 20 | 6f 66 20 74 68 65 73 65 |). None |of these|
|000047b0| 0d 0a 00 0d 0a 00 59 6f | 75 20 6d 61 79 20 77 61 |......Yo|u may wa|
|000047c0| 6e 74 20 74 6f 20 72 65 | 76 69 65 77 20 10 33 2d |nt to re|view .3-|
|000047d0| 31 2d 32 0e 69 33 2d 31 | 2d 32 0e 49 6e 74 65 67 |1-2.i3-1|-2.Integ|
|000047e0| 72 61 74 65 64 20 45 78 | 61 6d 70 6c 65 20 32 2e |rated Ex|ample 2.|
|000047f0| 0f 0d 0a 00 53 65 63 74 | 69 6f 6e 20 33 2e 31 20 |....Sect|ion 3.1 |
|00004800| 20 51 75 61 64 72 61 74 | 69 63 20 46 75 6e 63 74 | Quadrat|ic Funct|
|00004810| 69 6f 6e 73 20 20 20 20 | 20 20 20 20 20 20 20 20 |ions    |        |
|00004820| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00004830| 20 20 20 20 20 20 11 32 | 32 0d 0b 00 20 11 31 38 |      .2|2... .18|
|00004840| 2e 20 20 53 6b 65 74 63 | 68 20 74 68 65 20 67 72 |.  Sketc|h the gr|
|00004850| 61 70 68 20 6f 66 20 11 | 33 66 11 31 28 11 33 78 |aph of .|3f.1(.3x|
|00004860| 11 31 29 20 3d 20 2d 11 | 33 78 20 20 11 31 2b 20 |.1) = -.|3x  .1+ |
|00004870| 32 11 33 78 20 11 31 2b | 20 35 2e 20 20 49 64 65 |2.3x .1+| 5.  Ide|
|00004880| 6e 74 69 66 79 20 74 68 | 65 20 76 65 72 74 65 78 |ntify th|e vertex|
|00004890| 20 61 6e 64 20 0d 0a 00 | 20 20 20 20 20 69 6e 74 | and ...|     int|
|000048a0| 65 72 63 65 70 74 73 2e | 0d 0a 00 0d 0a 00 20 20 |ercepts.|......  |
|000048b0| 20 20 20 0e 61 34 2d 31 | 2d 32 35 61 0e 28 61 29 |   .a4-1|-25a.(a)|
|000048c0| 0f 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.       |        |
|000048d0| 20 20 20 20 20 0e 61 34 | 2d 31 2d 32 35 62 0e 28 |     .a4|-1-25b.(|
|000048e0| 62 29 0f 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |b).     |        |
|000048f0| 20 20 20 20 20 20 0e 61 | 34 2d 31 2d 32 35 63 0e |      .a|4-1-25c.|
|00004900| 28 63 29 0f 20 0d 0a 00 | 14 6a 34 2d 31 2d 32 35 |(c). ...|.j4-1-25|
|00004910| 61 2e 6d 14 39 14 37 14 | 32 30 14 37 14 20 20 14 |a.m.9.7.|20.7.  .|
|00004920| 6a 34 2d 31 2d 32 35 62 | 2e 6d 14 33 31 14 37 14 |j4-1-25b|.m.31.7.|
|00004930| 32 30 14 37 14 20 20 14 | 6a 34 2d 31 2d 32 35 63 |20.7.  .|j4-1-25c|
|00004940| 2e 6d 14 35 33 14 37 14 | 32 30 14 37 14 0d 0a 00 |.m.53.7.|20.7....|
|00004950| 0d 0a 00 0d 0a 00 0d 0a | 00 0d 0a 00 0d 0a 00 0d |........|........|
|00004960| 0b 00 20 20 20 20 20 20 | 20 20 20 56 65 72 74 65 |..      |   Verte|
|00004970| 78 3a 20 28 31 2c 20 34 | 29 20 20 20 20 20 20 20 |x: (1, 4|)       |
|00004980| 20 56 65 72 74 65 78 3a | 20 28 31 2c 20 36 29 20 | Vertex:| (1, 6) |
|00004990| 20 20 20 20 20 20 20 56 | 65 72 74 65 78 3a 20 28 |       V|ertex: (|
|000049a0| 2d 31 2c 20 34 29 0d 0a | 00 20 20 20 20 20 20 20 |-1, 4)..|.       |
|000049b0| 20 20 49 6e 74 65 72 63 | 65 70 74 73 3a 20 28 30 |  Interc|epts: (0|
|000049c0| 2c 20 33 29 20 20 20 20 | 49 6e 74 65 72 63 65 70 |, 3)    |Intercep|
|000049d0| 74 73 3a 20 28 30 2c 20 | 35 29 20 20 20 20 49 6e |ts: (0, |5)    In|
|000049e0| 74 65 72 63 65 70 74 3a | 20 28 30 2c 20 35 29 0d |tercept:| (0, 5).|
|000049f0| 0a 00 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |..      |        |
|00004a00| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00004a10| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 11 34 44 |        |     .4D|
|00004a20| 32 0d 0b 00 20 20 20 20 | 20 20 20 20 20 20 20 20 |2...    |        |
|00004a30| 11 31 28 33 2c 20 30 29 | 2c 20 28 2d 31 2c 20 30 |.1(3, 0)|, (-1, 0|
|00004a40| 29 20 20 20 20 20 20 20 | 20 20 20 28 31 20 11 34 |)       |   (1 .4|
|00004a50| 2b 20 53 20 11 31 36 2c | 20 30 29 20 0d 0a 00 0d |+ S .16,| 0) ....|
|00004a60| 0a 00 20 20 20 20 20 0e | 61 34 2d 31 2d 32 35 64 |..     .|a4-1-25d|
|00004a70| 0e 28 64 29 0f 20 4e 6f | 6e 65 20 6f 66 20 74 68 |.(d). No|ne of th|
|00004a80| 65 73 65 0d 0a 00 0d 0a | 00 59 6f 75 20 6d 61 79 |ese.....|.You may|
|00004a90| 20 77 61 6e 74 20 74 6f | 20 72 65 76 69 65 77 20 | want to| review |
|00004aa0| 10 33 2d 31 2d 32 0e 69 | 33 2d 31 2d 33 0e 49 6e |.3-1-2.i|3-1-3.In|
|00004ab0| 74 65 67 72 61 74 65 64 | 20 45 78 61 6d 70 6c 65 |tegrated| Example|
|00004ac0| 20 33 2e 0f 0d 0a 00 14 | 00 00 00 a5 02 00 00 50 | 3......|.......P|
|00004ad0| 00 04 00 14 00 00 00 10 | 00 00 00 61 34 2d 31 2d |........|...a4-1-|
|00004ae0| 31 31 61 00 bd 02 00 00 | a5 02 00 00 50 00 04 00 |11a.....|....P...|
|00004af0| bd 02 00 00 b9 02 00 00 | 61 34 2d 31 2d 31 31 62 |........|a4-1-11b|
|00004b00| 00 66 05 00 00 8f 00 00 | 00 50 00 04 00 66 05 00 |.f......|.P...f..|
|00004b10| 00 62 05 00 00 61 34 2d | 31 2d 31 31 63 00 f9 05 |.b...a4-|1-11c...|
|00004b20| 00 00 a5 02 00 00 50 00 | 04 00 f9 05 00 00 f5 05 |......P.|........|
|00004b30| 00 00 61 34 2d 31 2d 31 | 31 64 00 a2 08 00 00 cc |..a4-1-1|1d......|
|00004b40| 00 00 00 50 00 04 00 a2 | 08 00 00 9e 08 00 00 61 |...P....|.......a|
|00004b50| 34 2d 31 2d 31 37 61 00 | 72 09 00 00 cf 00 00 00 |4-1-17a.|r.......|
|00004b60| 50 00 04 00 72 09 00 00 | 6e 09 00 00 61 34 2d 31 |P...r...|n...a4-1|
|00004b70| 2d 31 37 62 00 45 0a 00 | 00 e3 00 00 00 50 00 04 |-17b.E..|.....P..|
|00004b80| 00 45 0a 00 00 41 0a 00 | 00 61 34 2d 31 2d 31 37 |.E...A..|.a4-1-17|
|00004b90| 63 00 2c 0b 00 00 36 00 | 00 00 50 00 04 00 2c 0b |c.,...6.|..P...,.|
|00004ba0| 00 00 28 0b 00 00 61 34 | 2d 31 2d 31 37 64 00 66 |..(...a4|-1-17d.f|
|00004bb0| 0b 00 00 6f 01 00 00 50 | 00 04 00 66 0b 00 00 62 |...o...P|...f...b|
|00004bc0| 0b 00 00 61 34 2d 31 2d | 31 39 61 00 d9 0c 00 00 |...a4-1-|19a.....|
|00004bd0| 67 01 00 00 50 00 04 00 | d9 0c 00 00 d5 0c 00 00 |g...P...|........|
|00004be0| 61 34 2d 31 2d 31 39 62 | 00 44 0e 00 00 4c 00 00 |a4-1-19b|.D...L..|
|00004bf0| 00 50 00 04 00 44 0e 00 | 00 40 0e 00 00 61 34 2d |.P...D..|.@...a4-|
|00004c00| 31 2d 31 39 63 00 94 0e | 00 00 39 00 00 00 50 00 |1-19c...|..9...P.|
|00004c10| 04 00 94 0e 00 00 90 0e | 00 00 61 34 2d 31 2d 31 |........|..a4-1-1|
|00004c20| 39 64 00 d1 0e 00 00 fb | 01 00 00 50 00 04 00 d1 |9d......|...P....|
|00004c30| 0e 00 00 cd 0e 00 00 61 | 34 2d 31 2d 32 35 61 00 |.......a|4-1-25a.|
|00004c40| d0 10 00 00 90 00 00 00 | 50 00 04 00 d0 10 00 00 |........|P.......|
|00004c50| cc 10 00 00 61 34 2d 31 | 2d 32 35 62 00 64 11 00 |....a4-1|-25b.d..|
|00004c60| 00 fb 01 00 00 50 00 04 | 00 64 11 00 00 60 11 00 |.....P..|.d...`..|
|00004c70| 00 61 34 2d 31 2d 32 35 | 63 00 63 13 00 00 39 00 |.a4-1-25|c.c...9.|
|00004c80| 00 00 50 00 04 00 63 13 | 00 00 5f 13 00 00 61 34 |..P...c.|.._...a4|
|00004c90| 2d 31 2d 32 35 64 00 a0 | 13 00 00 5a 00 00 00 50 |-1-25d..|...Z...P|
|00004ca0| 00 04 00 a0 13 00 00 9c | 13 00 00 61 34 2d 31 2d |........|...a4-1-|
|00004cb0| 32 37 61 00 fe 13 00 00 | e8 02 00 00 50 00 04 00 |27a.....|....P...|
|00004cc0| fe 13 00 00 fa 13 00 00 | 61 34 2d 31 2d 32 37 62 |........|a4-1-27b|
|00004cd0| 00 ea 16 00 00 e9 02 00 | 00 50 00 04 00 ea 16 00 |........|.P......|
|00004ce0| 00 e6 16 00 00 61 34 2d | 31 2d 32 37 63 00 d7 19 |.....a4-|1-27c...|
|00004cf0| 00 00 3a 00 00 00 50 00 | 04 00 d7 19 00 00 d3 19 |..:...P.|........|
|00004d00| 00 00 61 34 2d 31 2d 32 | 37 64 00 15 1a 00 00 02 |..a4-1-2|7d......|
|00004d10| 02 00 00 50 00 04 00 15 | 1a 00 00 11 1a 00 00 61 |...P....|.......a|
|00004d20| 34 2d 31 2d 33 33 61 00 | 1b 1c 00 00 02 02 00 00 |4-1-33a.|........|
|00004d30| 50 00 04 00 1b 1c 00 00 | 17 1c 00 00 61 34 2d 31 |P.......|....a4-1|
|00004d40| 2d 33 33 62 00 21 1e 00 | 00 98 00 00 00 50 00 04 |-33b.!..|.....P..|
|00004d50| 00 21 1e 00 00 1d 1e 00 | 00 61 34 2d 31 2d 33 33 |.!......|.a4-1-33|
|00004d60| 63 00 bd 1e 00 00 51 00 | 00 00 50 00 04 00 bd 1e |c.....Q.|..P.....|
|00004d70| 00 00 b9 1e 00 00 61 34 | 2d 31 2d 33 33 64 00 12 |......a4|-1-33d..|
|00004d80| 1f 00 00 0e 04 00 00 50 | 00 04 00 12 1f 00 00 0e |.......P|........|
|00004d90| 1f 00 00 61 34 2d 31 2d | 34 33 61 00 24 23 00 00 |...a4-1-|43a.$#..|
|00004da0| 0e 04 00 00 50 00 04 00 | 24 23 00 00 20 23 00 00 |....P...|$#.. #..|
|00004db0| 61 34 2d 31 2d 34 33 62 | 00 36 27 00 00 19 01 00 |a4-1-43b|.6'.....|
|00004dc0| 00 50 00 04 00 36 27 00 | 00 32 27 00 00 61 34 2d |.P...6'.|.2'..a4-|
|00004dd0| 31 2d 34 33 63 00 53 28 | 00 00 0e 04 00 00 50 00 |1-43c.S(|......P.|
|00004de0| 04 00 53 28 00 00 4f 28 | 00 00 61 34 2d 31 2d 34 |..S(..O(|..a4-1-4|
|00004df0| 33 64 00 65 2c 00 00 85 | 02 00 00 50 00 04 00 65 |3d.e,...|...P...e|
|00004e00| 2c 00 00 61 2c 00 00 61 | 34 2d 31 2d 37 61 00 ee |,..a,..a|4-1-7a..|
|00004e10| 2e 00 00 ad 00 00 00 50 | 00 04 00 ee 2e 00 00 ea |.......P|........|
|00004e20| 2e 00 00 61 34 2d 31 2d | 37 62 00 9f 2f 00 00 85 |...a4-1-|7b../...|
|00004e30| 02 00 00 50 00 04 00 9f | 2f 00 00 9b 2f 00 00 61 |...P....|/.../..a|
|00004e40| 34 2d 31 2d 37 63 00 28 | 32 00 00 85 02 00 00 50 |4-1-7c.(|2......P|
|00004e50| 00 04 00 28 32 00 00 24 | 32 00 00 61 34 2d 31 2d |...(2..$|2..a4-1-|
|00004e60| 37 64 00 cd 34 00 00 2c | 01 00 00 4d 20 00 00 ad |7d..4..,|...M ...|
|00004e70| 34 00 00 00 00 00 00 78 | 33 2d 31 00 19 36 00 00 |4......x|3-1..6..|
|00004e80| dd 01 00 00 4d 20 00 00 | f9 35 00 00 00 00 00 00 |....M ..|.5......|
|00004e90| 78 33 2d 31 2d 31 00 16 | 38 00 00 2f 02 00 00 4d |x3-1-1..|8../...M|
|00004ea0| 20 00 00 f6 37 00 00 00 | 00 00 00 78 33 2d 31 2d | ...7...|...x3-1-|
|00004eb0| 32 00 65 3a 00 00 35 02 | 00 00 4d 20 00 00 45 3a |2.e:..5.|..M ..E:|
|00004ec0| 00 00 00 00 00 00 78 33 | 2d 31 2d 33 00 ba 3c 00 |......x3|-1-3..<.|
|00004ed0| 00 7a 02 00 00 4d 20 00 | 00 9a 3c 00 00 00 00 00 |.z...M .|..<.....|
|00004ee0| 00 78 33 2d 31 2d 34 00 | 54 3f 00 00 ea 02 00 00 |.x3-1-4.|T?......|
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|00004f00| 2d 35 00 5e 42 00 00 e7 | 02 00 00 4d 20 00 00 3e |-5.^B...|...M ..>|
|00004f10| 42 00 00 00 00 00 00 78 | 33 2d 31 2d 36 00 65 45 |B......x|3-1-6.eE|
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|00004f30| 00 00 78 33 2d 31 2d 37 | 00 14 48 00 00 b3 02 00 |..x3-1-7|..H.....|
|00004f40| 00 4d 20 00 00 f4 47 00 | 00 00 00 00 00 78 33 2d |.M ...G.|.....x3-|
|00004f50| 31 2d 38 00             |                         |1-8.    |        |
+--------+-------------------------+-------------------------+--------+--------+