Interactive Algebra & Trigonometry - A Self Guided Study Companion

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|00000000| 54 55 54 4f 52 20 30 36 | 35 38 00 00 0c 01 00 00 |TUTOR 06|58......|
|00000010| 53 65 63 74 69 6f 6e 20 | 31 2e 31 20 20 47 72 61 |Section |1.1  Gra|
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|00000030| 20 55 74 69 6c 69 74 69 | 65 73 0d 0a 00 0d 0b 00 | Utiliti|es......|
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|00000050| 78 61 6d 70 6c 65 20 31 | 0f 20 20 56 65 72 69 66 |xample 1|.  Verif|
|00000060| 79 69 6e 67 20 53 6f 6c | 75 74 69 6f 6e 20 50 6f |ying Sol|ution Po|
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|00000080| 32 0e 47 75 69 64 65 64 | 20 45 78 61 6d 70 6c 65 |2.Guided| Example|
|00000090| 20 32 0f 20 20 46 69 6e | 64 69 6e 67 20 49 6e 74 | 2.  Fin|ding Int|
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|000000c0| 70 6c 65 20 33 0f 20 20 | 54 65 73 74 69 6e 67 20 |ple 3.  |Testing |
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|00000fa0| 20 20 20 20 20 20 20 79 | 20 11 31 3d 20 11 34 32 |       y| .1= .42|
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|00000ff0| 32 0d 0b 00 20 20 20 20 | 20 20 20 20 20 20 20 20 |2...    |        |
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|00001030| 20 11 31 2d 11 33 78 0d | 0b 00 20 20 20 20 20 20 | .1-.3x.|..      |
|00001040| 20 20 20 20 79 20 11 31 | 3d 20 11 34 32 32 32 32 |    y .1|= .42222|
|00001050| 32 32 32 32 32 20 11 31 | 3d 20 11 34 32 32 32 32 |22222 .1|= .42222|
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|00001070| 75 62 73 74 69 74 75 74 | 65 20 2d 78 20 66 6f 72 |ubstitut|e -x for|
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|000010f0| 20 20 13 0d 0a 00 0d 0b | 00 53 69 6e 63 65 20 74 |  ......|.Since t|
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|00001280| 20 20 20 20 32 0d 0b 00 | 20 20 20 20 20 20 20 20 |    2...|        |
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|00001320| 20 20 20 20 20 20 20 20 | 20 20 20 20 11 33 78 20 |        |    .3x |
|00001330| 20 11 31 2b 20 33 20 20 | 20 20 20 20 20 20 20 20 | .1+ 3  |        |
|00001340| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
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|00001390| 3d 20 11 34 32 32 32 32 | 32 32 32 20 20 20 20 20 |= .42222|222     |
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|00001550| 11 33 79 20 11 31 69 6e | 20 74 68 65 20 67 69 76 |.3y .1in| the giv|
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|00001570| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.       |        |
|00001580| 20 20 11 33 78 0d 0b 00 | 20 20 20 20 20 20 20 20 |  .3x...|        |
|00001590| 20 20 79 20 11 31 3d 20 | 11 34 32 32 32 32 32 32 |  y .1= |.4222222|
|000015a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000015b0| 20 20 20 20 20 11 32 12 | 31 47 69 76 65 6e 20 65 |     .2.|1Given e|
|000015c0| 71 75 61 74 69 6f 6e 12 | 30 0d 0b 00 20 20 20 20 |quation.|0...    |
|000015d0| 20 20 20 20 20 20 20 20 | 20 20 20 32 0d 0b 00 20 |        |   2... |
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|000015f0| 20 20 11 31 2b 20 33 13 | 0d 0a 00 20 20 20 20 20 |  .1+ 3.|...     |
|00001600| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 2d 11 33 |        |     -.3|
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|00001620| 0b 00 20 20 20 20 20 20 | 20 20 20 11 31 2d 11 33 |..      |   .1-.3|
|00001630| 79 20 11 31 3d 20 11 34 | 32 32 32 32 32 32 32 32 |y .1= .4|22222222|
|00001640| 32 20 11 31 3d 20 11 34 | 32 32 32 32 32 32 20 20 |2 .1= .4|222222  |
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|00001670| 2d 79 20 66 6f 72 20 79 | 12 30 0d 0b 00 20 20 20 |-y for y|.0...   |
|00001680| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 32 |        |       2|
|00001690| 20 20 20 20 20 20 20 20 | 32 0d 0b 00 20 20 20 20 |        |2...    |
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|000016c0| 20 11 31 2b 20 33 13 0d | 0a 00 20 20 20 20 20 20 | .1+ 3..|..      |
|000016d0| 20 20 20 20 20 20 20 20 | 20 20 20 11 33 78 0d 0b |        |   .3x..|
|000016e0| 00 20 20 20 20 20 20 20 | 20 20 20 79 20 11 31 3d |.       |   y .1=|
|000016f0| 20 11 34 32 32 32 32 32 | 32 20 20 20 20 20 20 20 | .422222|2       |
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|00001750| 20 11 33 78 20 20 11 31 | 2b 20 33 0d 0b 00 20 20 | .3x  .1|+ 3...  |
|00001760| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001770| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001780| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001790| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000017a0| 20 20 20 20 20 20 13 0d | 0a 00 53 69 6e 63 65 20 |      ..|..Since |
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|000017c0| 20 70 72 6f 64 75 63 65 | 73 20 61 6e 20 65 71 75 | produce|s an equ|
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|00001860| 47 72 61 70 68 69 6e 67 | 20 55 74 69 6c 69 74 69 |Graphing| Utiliti|
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|00001900| 20 6f 66 20 74 68 65 20 | 65 71 75 61 74 69 6f 6e | of the |equation|
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|00001920| 20 20 20 20 20 20 20 20 | 20 20 20 11 32 32 20 20 |        |   .22  |
|00001930| 20 20 20 20 20 20 20 20 | 32 20 20 20 20 32 0d 0b |        |2    2..|
|00001940| 00 20 20 20 20 20 11 31 | 28 11 33 78 20 11 31 2d |.     .1|(.3x .1-|
|00001950| 20 11 33 68 11 31 29 20 | 20 2b 20 28 11 33 79 20 | .3h.1) | + (.3y |
|00001960| 11 31 2d 20 11 33 6b 11 | 31 29 20 20 3d 20 11 33 |.1- .3k.|1)  = .3|
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|00001980| 11 33 68 11 31 2c 20 11 | 33 6b 11 31 29 20 69 73 |.3h.1, .|3k.1) is|
|00001990| 20 74 68 65 20 63 65 6e | 74 65 72 20 61 6e 64 20 | the cen|ter and |
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|000019d0| 33 2c 20 61 6e 64 0d 0a | 00 11 33 72 20 11 31 3d |3, and..|..3r .1=|
|000019e0| 20 34 2e 13 0d 0a 00 0d | 0b 00 54 68 65 6e 20 74 | 4......|..Then t|
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|00001a10| 20 62 65 63 6f 6d 65 73 | 0d 0a 00 0d 0b 00 20 20 | becomes|......  |
|00001a20| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001a30| 11 32 32 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.22     |        |
|00001a40| 32 20 20 20 20 32 0d 0b | 00 20 20 20 20 20 20 20 |2    2..|.       |
|00001a50| 20 20 20 20 11 31 28 11 | 33 78 20 11 31 2d 20 32 |    .1(.|3x .1- 2|
|00001a60| 29 20 20 2b 20 5b 11 33 | 79 20 11 31 2d 20 28 2d |)  + [.3|y .1- (-|
|00001a70| 33 29 5d 20 20 3d 20 34 | 20 13 0d 0a 00 0d 0b 00 |3)]  = 4| .......|
|00001a80| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001a90| 20 20 20 20 20 11 32 32 | 20 20 20 20 20 20 20 20 |     .22|        |
|00001aa0| 20 20 32 0d 0b 00 20 20 | 20 20 20 20 20 20 20 20 |  2...  |        |
|00001ab0| 20 20 20 20 11 31 28 11 | 33 78 20 11 31 2d 20 32 |    .1(.|3x .1- 2|
|00001ac0| 29 20 20 2b 20 28 11 33 | 79 20 11 31 2b 20 33 29 |)  + (.3|y .1+ 3)|
|00001ad0| 20 20 3d 20 31 36 2e 0d | 0a 00 53 65 63 74 69 6f |  = 16..|..Sectio|
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|00001b70| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
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|00001b90| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001ba0| 20 20 20 20 11 33 78 20 | 20 11 31 2b 20 11 33 79 |    .3x | .1+ .3y|
|00001bb0| 20 20 11 31 2b 20 32 11 | 33 78 20 11 31 2d 20 34 |  .1+ 2.|3x .1- 4|
|00001bc0| 11 33 79 20 11 31 2d 20 | 34 20 3d 20 30 0d 0a 00 |.3y .1- |4 = 0...|
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|00001be0| 0d 0a 00 0d 0b 00 57 65 | 20 62 65 67 69 6e 20 62 |......We| begin b|
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|00001c10| 6f 77 73 2e 0d 0a 00 0d | 0b 00 20 20 20 20 20 20 |ows.....|..      |
|00001c20| 20 20 20 20 20 20 20 11 | 32 32 20 20 20 20 32 0d |       .|22    2.|
|00001c30| 0b 00 20 20 20 20 20 20 | 20 20 20 20 20 20 11 33 |..      |      .3|
|00001c40| 78 20 20 11 31 2b 20 11 | 33 79 20 20 11 31 2b 20 |x  .1+ .|3y  .1+ |
|00001c50| 32 11 33 78 20 11 31 2d | 20 34 11 33 79 20 11 31 |2.3x .1-| 4.3y .1|
|00001c60| 2d 20 34 20 3d 20 30 20 | 20 20 20 20 20 20 20 20 |- 4 = 0 |        |
|00001c70| 20 20 20 20 11 32 12 31 | 47 65 6e 65 72 61 6c 20 |    .2.1|General |
|00001c80| 66 6f 72 6d 12 30 11 31 | 13 0d 0a 00 0d 0b 00 20 |form.0.1|....... |
|00001c90| 20 20 20 11 32 32 20 20 | 20 20 20 20 20 20 20 20 |   .22  |        |
|00001ca0| 20 20 20 20 20 20 32 0d | 0b 00 20 20 11 31 28 11 |      2.|..  .1(.|
|00001cb0| 33 78 20 20 11 31 2b 20 | 32 11 33 78 20 20 20 20 |3x  .1+ |2.3x    |
|00001cc0| 20 11 31 29 20 2b 20 28 | 11 33 79 20 20 11 31 2d | .1) + (|.3y  .1-|
|00001cd0| 20 34 11 33 79 20 20 20 | 20 20 11 31 29 20 3d 20 | 4.3y   |  .1) = |
|00001ce0| 34 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 32 |4       |      .2|
|00001cf0| 12 31 47 72 6f 75 70 20 | 74 65 72 6d 73 12 30 11 |.1Group |terms.0.|
|00001d00| 31 13 0d 0a 00 0d 0b 00 | 20 20 20 20 11 32 32 20 |1.......|    .22 |
|00001d10| 20 20 20 20 20 20 20 20 | 32 20 20 20 20 20 20 32 |        |2      2|
|00001d20| 20 20 20 20 20 20 20 20 | 20 32 0d 0b 00 20 20 11 |        | 2...  .|
|00001d30| 31 28 11 33 78 20 20 11 | 31 2b 20 32 78 20 2b 20 |1(.3x  .|1+ 2x + |
|00001d40| 31 20 29 20 2b 20 28 11 | 33 79 20 20 11 31 2d 20 |1 ) + (.|3y  .1- |
|00001d50| 34 11 33 79 20 11 31 2b | 20 32 20 29 20 3d 20 34 |4.3y .1+| 2 ) = 4|
|00001d60| 20 2b 20 31 20 2b 20 34 | 20 20 20 20 20 11 32 12 | + 1 + 4|     .2.|
|00001d70| 31 43 6f 6d 70 6c 65 74 | 65 20 74 68 65 20 73 71 |1Complet|e the sq|
|00001d80| 75 61 72 65 73 12 30 0d | 0a 00 20 20 20 20 20 20 |uares.0.|..      |
|00001d90| 20 20 11 31 12 31 11 34 | 21 20 20 20 20 5e 20 20 |  .1.1.4|!    ^  |
|00001da0| 20 20 20 20 20 20 20 20 | 20 21 20 20 20 20 5e 20 |        | !    ^ |
|00001db0| 11 31 12 30 0d 0b 00 20 | 20 20 20 20 20 20 20 12 |.1.0... |       .|
|00001dc0| 31 11 34 6c 32 32 32 32 | 6a 20 20 20 20 20 20 20 |1.4l2222|j       |
|00001dd0| 20 20 20 20 6c 32 32 32 | 32 6a 20 11 31 12 30 0d |    l222|2j .1.0.|
|00001de0| 0b 00 20 20 20 20 20 20 | 20 20 12 31 20 20 20 20 |..      |  .1    |
|00001df0| 20 20 11 32 32 20 20 20 | 20 20 20 20 20 20 20 20 |  .22   |        |
|00001e00| 20 20 20 20 20 32 11 31 | 12 30 0d 0b 00 20 20 20 |     2.1|.0...   |
|00001e10| 20 20 20 20 20 12 31 11 | 32 28 68 61 6c 66 29 20 |     .1.|2(half) |
|00001e20| 20 20 20 20 20 20 20 20 | 20 20 28 68 61 6c 66 29 |        |  (half)|
|00001e30| 20 11 31 12 30 20 20 20 | 20 20 20 20 20 20 20 20 | .1.0   |        |
|00001e40| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001e50| 20 20 20 20 20 20 20 20 | 20 20 20 13 0d 0a 00 20 |        |   .... |
|00001e60| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001e70| 20 20 20 20 11 32 32 20 | 20 20 20 20 20 20 20 20 |    .22 |        |
|00001e80| 20 32 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 20 | 2...   |        |
|00001e90| 20 20 20 11 31 28 11 33 | 78 20 11 31 2b 20 31 29 |   .1(.3|x .1+ 1)|
|00001ea0| 20 20 2b 20 28 11 33 79 | 20 11 31 2d 20 32 29 20 |  + (.3y| .1- 2) |
|00001eb0| 20 3d 20 39 20 20 20 20 | 20 20 20 20 20 20 20 20 | = 9    |        |
|00001ec0| 20 11 32 12 31 53 74 61 | 6e 64 61 72 64 20 66 6f | .2.1Sta|ndard fo|
|00001ed0| 72 6d 11 31 12 30 0d 0a | 00 0d 0a 00 46 72 6f 6d |rm.1.0..|....From|
|00001ee0| 20 74 68 69 73 20 73 74 | 61 6e 64 61 72 64 20 66 | this st|andard f|
|00001ef0| 6f 72 6d 2c 20 77 65 20 | 73 65 65 20 74 68 61 74 |orm, we |see that|
|00001f00| 20 74 68 65 20 63 65 6e | 74 65 72 20 6f 66 20 74 | the cen|ter of t|
|00001f10| 68 65 20 63 69 72 63 6c | 65 20 69 73 20 61 74 20 |he circl|e is at |
|00001f20| 74 68 65 0d 0a 00 70 6f | 69 6e 74 20 28 2d 31 2c |the...po|int (-1,|
|00001f30| 20 32 29 20 61 6e 64 20 | 74 68 65 20 72 61 64 69 | 2) and |the radi|
|00001f40| 75 73 20 6f 66 20 74 68 | 65 20 63 69 72 63 6c 65 |us of th|e circle|
|00001f50| 20 69 73 20 33 2e 13 0d | 0a 00 0d 0b 00 55 73 69 | is 3...|.....Usi|
|00001f60| 6e 67 20 74 68 69 73 20 | 69 6e 66 6f 72 6d 61 74 |ng this |informat|
|00001f70| 69 6f 6e 2c 20 77 65 20 | 73 6b 65 74 63 68 20 74 |ion, we |sketch t|
|00001f80| 68 65 20 67 72 61 70 68 | 20 6f 66 20 74 68 65 20 |he graph| of the |
|00001f90| 63 69 72 63 6c 65 20 61 | 73 20 73 68 6f 77 6e 20 |circle a|s shown |
|00001fa0| 62 65 6c 6f 77 2e 0d 0a | 00 20 20 20 20 20 20 20 |below...|.       |
|00001fb0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001fc0| 14 6b 33 2d 32 2d 39 2e | 6d 14 32 31 14 31 31 14 |.k3-2-9.|m.21.11.|
|00001fd0| 35 30 14 38 14 0d 0a 00 | 53 65 63 74 69 6f 6e 20 |50.8....|Section |
|00001fe0| 31 2e 31 20 20 47 72 61 | 70 68 73 20 61 6e 64 20 |1.1  Gra|phs and |
|00001ff0| 47 72 61 70 68 69 6e 67 | 20 55 74 69 6c 69 74 69 |Graphing| Utiliti|
|00002000| 65 73 0d 0b 00 53 6b 65 | 74 63 68 20 74 68 65 20 |es...Ske|tch the |
|00002010| 67 72 61 70 68 20 6f 66 | 20 11 33 79 20 11 31 3d |graph of| .3y .1=|
|00002020| 20 35 20 2d 20 32 11 33 | 78 11 31 2e 20 20 49 64 | 5 - 2.3|x.1.  Id|
|00002030| 65 6e 74 69 66 79 20 61 | 6e 79 20 69 6e 74 65 72 |entify a|ny inter|
|00002040| 63 65 70 74 73 20 61 6e | 64 20 74 65 73 74 20 66 |cepts an|d test f|
|00002050| 6f 72 0d 0a 00 73 79 6d | 6d 65 74 72 79 2e 0d 0a |or...sym|metry...|
|00002060| 00 0d 0b 00 13 12 31 53 | 4f 4c 55 54 49 4f 4e 12 |......1S|OLUTION.|
|00002070| 30 0d 0a 00 0d 0b 00 4c | 65 74 74 69 6e 67 20 11 |0......L|etting .|
|00002080| 33 78 20 11 31 3d 20 30 | 2c 20 77 65 20 73 65 65 |3x .1= 0|, we see|
|00002090| 20 74 68 61 74 20 74 68 | 65 20 11 33 79 11 31 2d | that th|e .3y.1-|
|000020a0| 69 6e 74 65 72 63 65 70 | 74 20 6f 63 63 75 72 73 |intercep|t occurs|
|000020b0| 20 61 74 20 28 30 2c 20 | 35 29 2e 0d 0a 00 0d 0b | at (0, |5)......|
|000020c0| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.       |        |
|000020d0| 20 20 20 20 20 20 20 20 | 20 11 33 79 20 11 31 3d |        | .3y .1=|
|000020e0| 20 35 20 2d 20 32 28 30 | 29 20 3d 20 35 13 0d 0a | 5 - 2(0|) = 5...|
|000020f0| 00 0d 0b 00 4c 65 74 74 | 69 6e 67 20 11 33 79 20 |....Lett|ing .3y |
|00002100| 11 31 3d 20 30 2c 20 77 | 65 20 73 65 65 20 74 68 |.1= 0, w|e see th|
|00002110| 61 74 20 74 68 65 20 11 | 33 78 11 31 2d 69 6e 74 |at the .|3x.1-int|
|00002120| 65 72 63 65 70 74 20 6f | 63 63 75 72 73 20 61 74 |ercept o|ccurs at|
|00002130| 20 28 35 2f 32 2c 20 30 | 29 2e 0d 0a 00 0d 0b 00 | (5/2, 0|).......|
|00002140| 20 20 20 20 20 20 20 20 | 20 20 20 30 20 3d 20 35 |        |   0 = 5|
|00002150| 20 2d 20 32 11 33 78 20 | 20 20 20 11 34 35 35 36 | - 2.3x |   .4556|
|00002160| 20 20 20 20 11 31 32 11 | 33 78 20 11 31 3d 20 35 |    .12.|3x .1= 5|
|00002170| 20 20 20 20 11 34 35 35 | 36 20 20 20 20 11 33 78 |    .455|6    .3x|
|00002180| 20 11 31 3d 20 35 2f 32 | 13 0d 0a 00 0d 0b 00 57 | .1= 5/2|.......W|
|00002190| 68 65 6e 20 77 65 20 74 | 65 73 74 20 66 6f 72 20 |hen we t|est for |
|000021a0| 73 79 6d 6d 65 74 72 79 | 2c 20 77 65 20 66 69 6e |symmetry|, we fin|
|000021b0| 64 20 74 68 61 74 20 61 | 6c 6c 20 74 68 72 65 65 |d that a|ll three|
|000021c0| 20 74 65 73 74 73 20 66 | 61 69 6c 2e 20 20 54 68 | tests f|ail.  Th|
|000021d0| 65 72 65 66 6f 72 65 2c | 20 77 65 0d 0a 00 63 6f |erefore,| we...co|
|000021e0| 6e 63 6c 75 64 65 20 74 | 68 61 74 20 74 68 65 20 |nclude t|hat the |
|000021f0| 67 72 61 70 68 20 64 6f | 65 73 6e 27 74 20 68 61 |graph do|esn't ha|
|00002200| 76 65 20 11 33 78 11 31 | 2d 61 78 69 73 2c 20 11 |ve .3x.1|-axis, .|
|00002210| 33 79 11 31 2d 61 78 69 | 73 2c 20 6f 72 20 6f 72 |3y.1-axi|s, or or|
|00002220| 69 67 69 6e 20 73 79 6d | 6d 65 74 72 79 2e 13 0d |igin sym|metry...|
|00002230| 0a 00 0d 0b 00 46 69 6e | 61 6c 6c 79 2c 20 75 73 |.....Fin|ally, us|
|00002240| 69 6e 67 20 61 20 74 61 | 62 6c 65 20 6f 66 20 76 |ing a ta|ble of v|
|00002250| 61 6c 75 65 73 20 61 6e | 64 20 74 68 65 20 74 77 |alues an|d the tw|
|00002260| 6f 20 69 6e 74 65 72 63 | 65 70 74 73 2c 20 77 65 |o interc|epts, we|
|00002270| 20 6f 62 74 61 69 6e 20 | 74 68 65 20 67 72 61 70 | obtain |the grap|
|00002280| 68 0d 0a 00 73 68 6f 77 | 6e 20 6f 6e 20 74 68 65 |h...show|n on the|
|00002290| 20 6e 65 78 74 20 70 61 | 67 65 2e 0d 0a 00 0d 0a | next pa|ge......|
|000022a0| 00 0d 0a 00 0d 0a 00 0d | 0a 00 20 20 20 20 20 20 |........|..      |
|000022b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000022c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000022d0| 20 20 20 20 0d 0b 00 20 | 20 20 20 20 11 34 5b 32 |    ... |    .4[2|
|000022e0| 32 32 32 32 32 32 32 32 | 32 32 32 32 32 32 32 32 |22222222|22222222|
|000022f0| 32 32 32 32 32 32 32 32 | 32 32 32 32 32 5d 0d 0b |22222222|22222]..|
|00002300| 00 20 20 20 20 20 21 20 | 11 33 78 20 20 20 20 20 |.     ! |.3x     |
|00002310| 20 20 20 20 20 11 34 21 | 20 11 31 2d 32 20 11 34 |     .4!| .1-2 .4|
|00002320| 21 20 11 31 2d 31 20 11 | 34 21 20 11 31 31 20 11 |! .1-1 .|4! .11 .|
|00002330| 34 21 20 11 31 32 20 11 | 34 21 0d 0b 00 20 20 20 |4! .12 .|4!...   |
|00002340| 20 20 21 32 32 32 32 32 | 32 32 32 32 32 32 32 32 |  !22222|22222222|
|00002350| 32 32 32 32 32 32 32 32 | 32 32 32 32 32 32 32 32 |22222222|22222222|
|00002360| 32 21 0d 0b 00 20 20 20 | 20 20 21 20 11 33 79 20 |2!...   |  ! .3y |
|00002370| 11 31 3d 20 35 20 2d 20 | 32 11 33 78 20 11 34 21 |.1= 5 - |2.3x .4!|
|00002380| 20 20 11 31 39 20 11 34 | 21 20 20 11 31 37 20 11 |  .19 .4|!  .17 .|
|00002390| 34 21 20 11 31 33 20 11 | 34 21 20 11 31 31 20 11 |4! .13 .|4! .11 .|
|000023a0| 34 21 20 0d 0b 00 20 20 | 20 20 20 6c 32 32 32 32 |4! ...  |   l2222|
|000023b0| 32 32 32 32 32 32 32 32 | 32 32 32 32 32 32 32 32 |22222222|22222222|
|000023c0| 32 32 32 32 32 32 32 32 | 32 32 6a 0d 0a 00 20 20 |22222222|22j...  |
|000023d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000023e0| 20 20 20 20 20 11 31 14 | 6b 33 2d 32 2d 34 2e 6d |     .1.|k3-2-4.m|
|000023f0| 14 34 35 14 32 14 35 30 | 14 38 14 0d 0a 00 53 65 |.45.2.50|.8....Se|
|00002400| 63 74 69 6f 6e 20 31 2e | 31 20 20 47 72 61 70 68 |ction 1.|1  Graph|
|00002410| 73 20 61 6e 64 20 47 72 | 61 70 68 69 6e 67 20 55 |s and Gr|aphing U|
|00002420| 74 69 6c 69 74 69 65 73 | 0d 0b 00 20 20 20 20 20 |tilities|...     |
|00002430| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002440| 20 20 20 20 11 32 32 0d | 0b 00 11 31 53 6b 65 74 |    .22.|...1Sket|
|00002450| 63 68 20 74 68 65 20 67 | 72 61 70 68 20 6f 66 20 |ch the g|raph of |
|00002460| 11 33 79 20 11 31 3d 20 | 11 33 78 20 20 11 31 2d |.3y .1= |.3x  .1-|
|00002470| 20 11 33 78 20 11 31 2d | 20 36 2e 20 20 49 64 65 | .3x .1-| 6.  Ide|
|00002480| 6e 74 69 66 79 20 61 6e | 79 20 69 6e 74 65 72 63 |ntify an|y interc|
|00002490| 65 70 74 73 20 61 6e 64 | 20 74 65 73 74 20 66 6f |epts and| test fo|
|000024a0| 72 20 0d 0a 00 73 79 6d | 6d 65 74 72 79 2e 0d 0a |r ...sym|metry...|
|000024b0| 00 0d 0a 00 13 12 31 53 | 4f 4c 55 54 49 4f 4e 12 |......1S|OLUTION.|
|000024c0| 30 0d 0a 00 0d 0b 00 4c | 65 74 74 69 6e 67 20 11 |0......L|etting .|
|000024d0| 33 78 20 11 31 3d 20 30 | 2c 20 77 65 20 73 65 65 |3x .1= 0|, we see|
|000024e0| 20 74 68 61 74 20 74 68 | 65 20 11 33 79 11 31 2d | that th|e .3y.1-|
|000024f0| 69 6e 74 65 72 63 65 70 | 74 20 6f 63 63 75 72 73 |intercep|t occurs|
|00002500| 20 61 74 20 28 30 2c 20 | 2d 36 29 2e 0d 0a 00 20 | at (0, |-6).... |
|00002510| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002520| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 32 |        |      .2|
|00002530| 32 0d 0b 00 20 20 20 20 | 20 20 20 20 20 20 20 20 |2...    |        |
|00002540| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 33 |        |      .3|
|00002550| 79 20 11 31 3d 20 30 20 | 20 2d 20 30 20 2d 20 36 |y .1= 0 | - 0 - 6|
|00002560| 20 3d 20 2d 36 13 0d 0a | 00 0d 0b 00 4c 65 74 74 | = -6...|....Lett|
|00002570| 69 6e 67 20 11 33 79 20 | 11 31 3d 20 30 2c 20 77 |ing .3y |.1= 0, w|
|00002580| 65 20 73 65 65 20 74 68 | 61 74 20 74 68 65 20 11 |e see th|at the .|
|00002590| 33 78 11 31 2d 69 6e 74 | 65 72 63 65 70 74 73 20 |3x.1-int|ercepts |
|000025a0| 6f 63 63 75 72 20 61 74 | 20 28 2d 32 2c 20 30 29 |occur at| (-2, 0)|
|000025b0| 20 61 6e 64 20 28 33 2c | 20 30 29 2e 0d 0a 00 20 | and (3,| 0).... |
|000025c0| 20 20 20 20 20 20 20 20 | 20 20 20 11 32 32 0d 0b |        |   .22..|
|000025d0| 00 20 20 20 20 20 20 20 | 11 31 30 20 3d 20 11 33 |.       |.10 = .3|
|000025e0| 78 20 20 11 31 2d 20 11 | 33 78 20 11 31 2d 20 36 |x  .1- .|3x .1- 6|
|000025f0| 20 20 20 11 34 35 35 36 | 20 20 20 11 31 30 20 3d |   .4556|   .10 =|
|00002600| 20 28 11 33 78 20 11 31 | 2b 20 32 29 28 11 33 78 | (.3x .1|+ 2)(.3x|
|00002610| 20 11 31 2d 20 33 29 20 | 20 20 11 34 35 35 36 20 | .1- 3) |  .4556 |
|00002620| 20 20 11 33 78 20 11 31 | 3d 20 2d 32 2c 20 33 13 |  .3x .1|= -2, 3.|
|00002630| 0d 0a 00 0d 0b 00 57 68 | 65 6e 20 77 65 20 74 65 |......Wh|en we te|
|00002640| 73 74 20 66 6f 72 20 73 | 79 6d 6d 65 74 72 79 2c |st for s|ymmetry,|
|00002650| 20 77 65 20 66 69 6e 64 | 20 74 68 61 74 20 61 6c | we find| that al|
|00002660| 6c 20 74 68 72 65 65 20 | 74 65 73 74 73 20 66 61 |l three |tests fa|
|00002670| 69 6c 2e 20 20 54 68 65 | 72 65 66 6f 72 65 2c 20 |il.  The|refore, |
|00002680| 77 65 0d 0a 00 63 6f 6e | 63 6c 75 64 65 20 74 68 |we...con|clude th|
|00002690| 61 74 20 74 68 65 20 67 | 72 61 70 68 20 64 6f 65 |at the g|raph doe|
|000026a0| 73 6e 27 74 20 68 61 76 | 65 20 11 33 78 11 31 2d |sn't hav|e .3x.1-|
|000026b0| 61 78 69 73 2c 20 11 33 | 79 11 31 2d 61 78 69 73 |axis, .3|y.1-axis|
|000026c0| 2c 20 6f 72 20 6f 72 69 | 67 69 6e 20 73 79 6d 6d |, or ori|gin symm|
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|000026e0| 6c 6c 79 2c 20 75 73 69 | 6e 67 20 61 20 74 61 62 |lly, usi|ng a tab|
|000026f0| 6c 65 20 6f 66 20 76 61 | 6c 75 65 73 20 61 6e 64 |le of va|lues and|
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|00002720| 20 74 68 65 0d 0a 00 67 | 72 61 70 68 20 73 68 6f | the...g|raph sho|
|00002730| 77 6e 20 6f 6e 20 74 68 | 65 20 6e 65 78 74 20 70 |wn on th|e next p|
|00002740| 61 67 65 2e 0d 0a 00 0d | 0a 00 0d 0a 00 0d 0a 00 |age.....|........|
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|00002760| 32 32 32 32 32 32 32 32 | 32 32 32 32 32 32 32 32 |22222222|22222222|
|00002770| 32 32 32 32 32 32 32 32 | 32 32 32 32 32 32 5d 0d |22222222|222222].|
|00002780| 0b 00 20 21 20 20 20 20 | 20 20 20 20 20 20 20 20 |.. !    |        |
|00002790| 20 20 20 20 21 20 20 20 | 20 21 20 20 20 20 21 20 |    !   | !    ! |
|000027a0| 20 20 20 21 20 20 20 20 | 21 0d 0b 00 20 21 20 11 |   !    |!... ! .|
|000027b0| 33 78 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |3x      |        |
|000027c0| 11 34 21 20 11 31 2d 33 | 20 11 34 21 20 11 31 2d |.4! .1-3| .4! .1-|
|000027d0| 31 20 11 34 21 20 20 11 | 31 31 20 11 34 21 20 20 |1 .4!  .|11 .4!  |
|000027e0| 11 31 32 20 11 34 21 0d | 0b 00 20 21 32 32 32 32 |.12 .4!.|.. !2222|
|000027f0| 32 32 32 32 32 32 32 32 | 32 32 32 32 32 32 32 32 |22222222|22222222|
|00002800| 32 32 32 32 32 32 32 32 | 32 32 32 32 32 32 32 32 |22222222|22222222|
|00002810| 21 0d 0b 00 20 21 20 20 | 20 20 20 20 11 32 32 20 |!... !  |    .22 |
|00002820| 20 20 20 20 20 20 20 20 | 11 34 21 20 20 20 20 21 |        |.4!    !|
|00002830| 20 20 20 20 21 20 20 20 | 20 21 20 20 20 20 21 0d |    !   | !    !.|
|00002840| 0b 00 20 21 20 11 33 79 | 20 11 31 3d 20 11 33 78 |.. ! .3y| .1= .3x|
|00002850| 20 20 11 31 2d 20 11 33 | 78 20 11 31 2d 20 36 20 |  .1- .3|x .1- 6 |
|00002860| 11 34 21 20 20 11 31 36 | 20 11 34 21 20 11 31 2d |.4!  .16| .4! .1-|
|00002870| 34 20 11 34 21 20 11 31 | 2d 36 20 11 34 21 20 11 |4 .4! .1|-6 .4! .|
|00002880| 31 2d 34 20 11 34 21 20 | 20 20 20 0d 0b 00 20 6c |1-4 .4! |   ... l|
|00002890| 32 32 32 32 32 32 32 32 | 32 32 32 32 32 32 32 32 |22222222|22222222|
|000028a0| 32 32 32 32 32 32 32 32 | 32 32 32 32 32 32 32 32 |22222222|22222222|
|000028b0| 32 32 32 32 6a 0d 0a 00 | 20 20 20 20 20 20 20 20 |2222j...|        |
|000028c0| 20 20 20 20 20 20 20 11 | 31 14 76 6b 33 2d 32 2d |       .|1.vk3-2-|
|000028d0| 35 61 2e 6d 14 34 36 14 | 32 14 35 30 14 38 14 14 |5a.m.46.|2.50.8..|
|000028e0| 76 6b 33 2d 32 2d 35 62 | 2e 6d 14 34 36 14 32 14 |vk3-2-5b|.m.46.2.|
|000028f0| 35 30 14 38 14 14 76 6b | 33 2d 32 2d 35 63 2e 6d |50.8..vk|3-2-5c.m|
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|00002910| 32 2d 35 64 2e 6d 14 34 | 36 14 32 14 35 30 14 38 |2-5d.m.4|6.2.50.8|
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|00002950| 14 76 6b 33 2d 32 2d 35 | 67 2e 6d 14 34 36 14 32 |.vk3-2-5|g.m.46.2|
|00002960| 14 35 30 14 38 14 14 76 | 6b 33 2d 32 2d 35 68 2e |.50.8..v|k3-2-5h.|
|00002970| 6d 14 34 36 14 32 14 35 | 30 14 38 14 14 76 6b 33 |m.46.2.5|0.8..vk3|
|00002980| 2d 32 2d 35 69 2e 6d 14 | 34 36 14 32 14 35 30 14 |-2-5i.m.|46.2.50.|
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|000029a0| 20 20 47 72 61 70 68 73 | 20 61 6e 64 20 47 72 61 |  Graphs| and Gra|
|000029b0| 70 68 69 6e 67 20 55 74 | 69 6c 69 74 69 65 73 0d |phing Ut|ilities.|
|000029c0| 0b 00 53 6b 65 74 63 68 | 20 74 68 65 20 67 72 61 |..Sketch| the gra|
|000029d0| 70 68 20 6f 66 20 11 33 | 79 20 11 31 3d 20 7c 11 |ph of .3|y .1= |.|
|000029e0| 33 78 11 31 7c 20 2b 20 | 32 2e 20 20 49 64 65 6e |3x.1| + |2.  Iden|
|000029f0| 74 69 66 79 20 61 6e 79 | 20 69 6e 74 65 72 63 65 |tify any| interce|
|00002a00| 70 74 73 20 61 6e 64 20 | 74 65 73 74 20 66 6f 72 |pts and |test for|
|00002a10| 20 0d 0a 00 73 79 6d 6d | 65 74 72 79 2e 0d 0a 00 | ...symm|etry....|
|00002a20| 0d 0b 00 13 12 31 53 4f | 4c 55 54 49 4f 4e 12 30 |.....1SO|LUTION.0|
|00002a30| 0d 0a 00 0d 0b 00 4c 65 | 74 74 69 6e 67 20 11 33 |......Le|tting .3|
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|00002a90| 20 20 20 20 20 20 20 11 | 33 79 20 11 31 3d 20 7c |       .|3y .1= ||
|00002aa0| 30 7c 20 2b 20 32 20 3d | 20 32 13 0d 0a 00 0d 0b |0| + 2 =| 2......|
|00002ab0| 00 4c 65 74 74 69 6e 67 | 20 11 33 79 20 11 31 3d |.Letting| .3y .1=|
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|00002ae0| 68 61 73 20 6e 6f 20 72 | 65 61 6c 20 73 6f 6c 75 |has no r|eal solu|
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|00002b10| 6e 6f 20 11 33 78 11 31 | 2d 69 6e 74 65 72 63 65 |no .3x.1|-interce|
|00002b20| 70 74 73 2e 0d 0a 00 0d | 0b 00 20 20 20 20 20 20 |pts.....|..      |
|00002b30| 20 20 20 20 20 20 20 20 | 20 20 20 30 20 3d 20 7c |        |   0 = ||
|00002b40| 11 33 78 11 31 7c 20 2b | 20 32 20 20 20 11 34 35 |.3x.1| +| 2   .45|
|00002b50| 35 36 20 20 20 11 31 2d | 32 20 3d 20 7c 11 33 78 |56   .1-|2 = |.3x|
|00002b60| 11 31 7c 20 20 20 20 20 | 20 12 31 11 32 4e 6f 20 |.1|     | .1.2No |
|00002b70| 72 65 61 6c 20 73 6f 6c | 75 74 69 6f 6e 73 11 31 |real sol|utions.1|
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|00002bf0| 11 31 2d 61 78 69 73 20 | 73 79 6d 6d 65 74 72 79 |.1-axis |symmetry|
|00002c00| 2e 0d 0a 00 0d 0b 00 20 | 20 20 20 20 20 20 20 20 |....... |        |
|00002c10| 20 20 20 11 33 79 20 11 | 31 3d 20 7c 11 33 78 11 |   .3y .|1= |.3x.|
|00002c20| 31 7c 20 2b 20 32 20 20 | 20 20 20 20 20 20 20 20 |1| + 2  |        |
|00002c30| 20 20 20 20 20 12 31 11 | 32 47 69 76 65 6e 20 65 |     .1.|2Given e|
|00002c40| 71 75 61 74 69 6f 6e 11 | 31 12 30 13 0d 0a 00 0d |quation.|1.0.....|
|00002c50| 0b 00 20 20 20 20 20 20 | 20 20 20 20 20 20 11 33 |..      |      .3|
|00002c60| 79 20 11 31 3d 20 7c 2d | 11 33 78 11 31 7c 20 2b |y .1= |-|.3x.1| +|
|00002c70| 20 32 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | 2      |        |
|00002c80| 12 31 11 32 52 65 70 6c | 61 63 65 20 78 20 62 79 |.1.2Repl|ace x by|
|00002c90| 20 2d 78 11 31 12 30 13 | 0d 0a 00 0d 0b 00 20 20 | -x.1.0.|......  |
|00002ca0| 20 20 20 20 20 20 20 20 | 20 20 11 33 79 20 11 31 |        |  .3y .1|
|00002cb0| 3d 20 7c 11 33 78 11 31 | 7c 20 2b 20 32 20 20 20 |= |.3x.1|| + 2   |
|00002cc0| 20 20 20 20 20 20 20 20 | 20 20 20 20 12 31 11 32 |        |    .1.2|
|00002cd0| 52 65 70 6c 61 63 65 6d | 65 6e 74 20 79 69 65 6c |Replacem|ent yiel|
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|00002cf0| 75 61 74 69 6f 6e 11 31 | 12 30 0d 0a 00 0d 0b 00 |uation.1|.0......|
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|00002d30| 20 11 33 79 11 31 2d 61 | 78 69 73 2e 13 0d 0a 00 | .3y.1-a|xis.....|
|00002d40| 0d 0b 00 55 73 69 6e 67 | 20 73 79 6d 6d 65 74 72 |...Using| symmetr|
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|00002d80| 74 20 6f 66 20 74 68 65 | 20 11 33 79 11 31 2d 61 |t of the| .3y.1-a|
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|00002db0| 62 74 61 69 6e 20 74 68 | 65 20 64 65 73 69 72 65 |btain th|e desire|
|00002dc0| 64 20 67 72 61 70 68 20 | 61 73 20 73 68 6f 77 6e |d graph |as shown|
|00002dd0| 20 62 65 6c 6f 77 2e 0d | 0a 00 0d 0a 00 0d 0a 00 | below..|........|
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|00002e20| 20 20 21 20 20 20 21 0d | 0b 00 20 20 21 20 11 33 |  !   !.|..  ! .3|
|00002e30| 78 20 20 20 20 20 20 20 | 20 20 20 20 11 34 21 20 |x       |    .4! |
|00002e40| 11 31 31 20 11 34 21 20 | 11 31 32 20 11 34 21 20 |.11 .4! |.12 .4! |
|00002e50| 11 31 33 20 11 34 21 20 | 11 31 34 20 11 34 21 0d |.13 .4! |.14 .4!.|
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|00003030| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003040| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003050| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003060| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
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|000030a0| 20 20 20 2e 0d 0a 00 53 | 65 63 74 69 6f 6e 20 31 |   ....S|ection 1|
|000030b0| 2e 31 20 20 47 72 61 70 | 68 73 20 61 6e 64 20 47 |.1  Grap|hs and G|
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|000030d0| 73 0d 0b 00 20 20 20 20 | 20 20 20 20 20 20 20 20 |s...    |        |
|000030e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000030f0| 20 11 32 32 0d 0b 00 11 | 31 53 6b 65 74 63 68 20 | .22....|1Sketch |
|00003100| 74 68 65 20 67 72 61 70 | 68 20 6f 66 20 11 33 78 |the grap|h of .3x|
|00003110| 20 11 31 3d 20 31 20 2d | 20 11 33 79 20 11 31 2e | .1= 1 -| .3y .1.|
|00003120| 20 20 49 64 65 6e 74 69 | 66 79 20 61 6e 79 20 69 |  Identi|fy any i|
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|00003150| 72 79 2e 0d 0a 00 0d 0b | 00 13 12 31 53 4f 4c 55 |ry......|...1SOLU|
|00003160| 54 49 4f 4e 12 30 0d 0a | 00 0d 0b 00 4c 65 74 74 |TION.0..|....Lett|
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|00003180| 65 20 73 65 65 20 74 68 | 61 74 20 74 68 65 20 11 |e see th|at the .|
|00003190| 33 79 11 31 2d 69 6e 74 | 65 72 63 65 70 74 73 20 |3y.1-int|ercepts |
|000031a0| 6f 63 63 75 72 20 61 74 | 20 28 30 2c 20 31 29 20 |occur at| (0, 1) |
|000031b0| 61 6e 64 20 28 30 2c 20 | 2d 31 29 2e 0d 0a 00 20 |and (0, |-1).... |
|000031c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000031d0| 20 20 20 20 20 11 32 32 | 20 20 20 20 20 20 20 20 |     .22|        |
|000031e0| 20 20 20 20 32 0d 0b 00 | 20 20 20 20 20 20 20 20 |    2...|        |
|000031f0| 20 20 20 20 20 11 31 30 | 20 3d 20 31 20 2d 20 11 |     .10| = 1 - .|
|00003200| 33 79 20 20 20 20 20 11 | 34 35 35 36 20 20 20 20 |3y     .|4556    |
|00003210| 11 33 79 20 20 11 31 3d | 20 31 20 20 20 20 11 34 |.3y  .1=| 1    .4|
|00003220| 35 35 36 20 20 20 20 11 | 33 79 20 11 31 3d 20 11 |556    .|3y .1= .|
|00003230| 34 2b 11 31 31 13 0d 0a | 00 0d 0b 00 4c 65 74 74 |4+.11...|....Lett|
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|00003260| 33 78 11 31 2d 69 6e 74 | 65 72 63 65 70 74 20 6f |3x.1-int|ercept o|
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|000032a0| 20 20 20 20 20 11 32 32 | 0d 0b 00 20 20 20 20 20 |     .22|...     |
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|000032c0| 20 20 20 20 11 33 78 20 | 11 31 3d 20 31 20 2d 20 |    .3x |.1= 1 - |
|000032d0| 30 20 20 3d 20 31 13 0d | 0a 00 0d 0b 00 4f 66 20 |0  = 1..|.....Of |
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|000032f0| 66 6f 72 20 73 79 6d 6d | 65 74 72 79 2c 20 74 68 |for symm|etry, th|
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|00003320| 74 68 69 73 20 0d 0a 00 | 65 71 75 61 74 69 6f 6e |this ...|equation|
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|00003340| 20 11 33 78 11 31 2d 61 | 78 69 73 20 73 79 6d 6d | .3x.1-a|xis symm|
|00003350| 65 74 72 79 2e 0d 0a 00 | 20 20 20 20 20 20 20 20 |etry....|        |
|00003360| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 11 32 32 |        |     .22|
|00003370| 0d 0b 00 20 20 20 20 20 | 20 20 20 20 20 20 20 11 |...     |       .|
|00003380| 33 78 20 11 31 3d 20 31 | 20 2d 20 11 33 79 20 20 |3x .1= 1| - .3y  |
|00003390| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000033a0| 11 31 12 31 11 32 47 69 | 76 65 6e 20 65 71 75 61 |.1.1.2Gi|ven equa|
|000033b0| 74 69 6f 6e 11 31 12 30 | 13 0d 0a 00 20 20 20 20 |tion.1.0|....    |
|000033c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000033d0| 20 20 20 20 11 32 32 0d | 0b 00 20 20 20 20 20 20 |    .22.|..      |
|000033e0| 20 20 20 20 20 20 11 33 | 78 20 11 31 3d 20 31 20 |      .3|x .1= 1 |
|000033f0| 2d 20 28 2d 11 33 79 11 | 31 29 20 20 20 20 20 20 |- (-.3y.|1)      |
|00003400| 20 20 20 20 20 20 20 20 | 20 12 31 11 32 52 65 70 |        | .1.2Rep|
|00003410| 6c 61 63 65 20 79 20 77 | 69 74 68 20 2d 79 11 31 |lace y w|ith -y.1|
|00003420| 12 30 13 0d 0a 00 20 20 | 20 20 20 20 20 20 20 20 |.0....  |        |
|00003430| 20 20 20 20 20 20 20 20 | 20 20 20 11 32 32 0d 0b |        |   .22..|
|00003440| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 11 33 78 |.       |     .3x|
|00003450| 20 11 31 3d 20 31 20 2d | 20 11 33 79 20 20 20 20 | .1= 1 -| .3y    |
|00003460| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 31 |        |      .1|
|00003470| 12 31 11 32 52 65 70 6c | 61 63 65 6d 65 6e 74 20 |.1.2Repl|acement |
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|000034c0| 20 77 69 74 68 20 72 65 | 73 70 65 63 74 20 74 6f | with re|spect to|
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|000035b0| 20 11 32 32 20 20 11 34 | 21 20 20 20 20 20 21 20 | .22  .4|!     ! |
|000035c0| 20 20 20 21 20 20 20 20 | 21 0d 0b 00 20 20 21 20 |   !    |!...  ! |
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|000035f0| 11 31 2d 38 20 11 34 21 | 20 11 31 2d 33 20 11 34 |.1-8 .4!| .1-3 .4|
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|00003650| 11 33 79 20 20 20 20 20 | 20 20 20 20 20 20 11 34 |.3y     |      .4|
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|000037b0| 0b 00 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |..      |        |
|000037c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000037d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000037e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000037f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003800| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003810| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003820| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003830| 20 2e 0d 0a 00 3a 00 00 | 00 94 02 00 00 4d 2a 00 | ....:..|.....M*.|
|00003840| 00 10 00 00 00 00 00 00 | 00 65 31 2d 31 00 f8 02 |........|.e1-1...|
|00003850| 00 00 c2 05 00 00 4d 2a | 00 00 ce 02 00 00 00 00 |......M*|........|
|00003860| 00 00 65 31 2d 31 2d 31 | 00 e4 08 00 00 12 05 00 |..e1-1-1|........|
|00003870| 00 4d 2a 00 00 ba 08 00 | 00 00 00 00 00 65 31 2d |.M*.....|.....e1-|
|00003880| 31 2d 32 00 20 0e 00 00 | 28 0a 00 00 4d 2a 00 00 |1-2. ...|(...M*..|
|00003890| f6 0d 00 00 00 00 00 00 | 65 31 2d 31 2d 33 00 72 |........|e1-1-3.r|
|000038a0| 18 00 00 68 02 00 00 4d | 2a 00 00 48 18 00 00 00 |...h...M|*..H....|
|000038b0| 00 00 00 65 31 2d 31 2d | 34 00 04 1b 00 00 d4 04 |...e1-1-|4.......|
|000038c0| 00 00 4d 2a 00 00 da 1a | 00 00 00 00 00 00 65 31 |..M*....|......e1|
|000038d0| 2d 31 2d 35 00 02 20 00 | 00 fc 03 00 00 4d 2a 00 |-1-5.. .|.....M*.|
|000038e0| 00 d8 1f 00 00 00 00 00 | 00 69 31 2d 31 2d 31 00 |........|.i1-1-1.|
|000038f0| 28 24 00 00 6d 05 00 00 | 4d 2a 00 00 fe 23 00 00 |($..m...|M*...#..|
|00003900| 00 00 00 00 69 31 2d 31 | 2d 32 00 bf 29 00 00 e8 |....i1-1|-2..)...|
|00003910| 06 00 00 4d 2a 00 00 95 | 29 00 00 00 00 00 00 69 |...M*...|)......i|
|00003920| 31 2d 31 2d 33 00 d1 30 | 00 00 64 07 00 00 4d 2a |1-1-3..0|..d...M*|
|00003930| 00 00 a7 30 00 00 00 00 | 00 00 69 31 2d 31 2d 34 |...0....|..i1-1-4|
|00003940| 00                      |                         |.       |        |
+--------+-------------------------+-------------------------+--------+--------+