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Thread: how would i even begin to solve this..plzz help

  1. #1
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    Exclamation how would i even begin to solve this..plzz help

    how would i sketch something like this?

    y= -4 | x+7 | + 20 and indicate its vertex and all intercepts

    i am thinking that i should add 4 to both sides making it |x+7|+24??

    i don't know how to solve this...(this is so hopeless for me)
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  2. #2
    Senior Member Stroodle's Avatar
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    One way to sketch it is to first sketch the graph of y=x+7, remembering to reflect the part of the graph that is below the x-axis. Then apply the dilation of -4 (multiply each value by -4, this will reflect the entire graph in the x-axis) After this you can then translate the graph 24 units in the positive direction of the y-axis.
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  3. #3
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    earboth's Avatar
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    Quote Originally Posted by Candy101 View Post
    how would i sketch something like this?

    y= -4 | x+7 | + 20 and indicate its vertex and all intercepts

    i am thinking that i should add 4 to both sides making it |x+7|+24??

    i don't know how to solve this...(this is so hopeless for me)
    1. The smallest value an absolute value can get is zero. This happens here at x = -7. Then the y-coordinate is 20. This is your vertex V(-7, 20).

    2. The y-intercept is at x = 0; then y = -4 \cdot |7| + 20 = -8

    3. The x-intercepts are at y = 0. Thus you have to solve for x:

    -4 |x+7| + 20 = 0
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  4. #4
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    ok so do i

    add 4

    making it |x+7|+24???
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  5. #5
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    Helloo, Candy101!

    How would i sketch something like this?

    y \:=\: -4|x+7| + 20 . and indicate its vertex and all intercepts

    We are expected to know the graph of: y \:=\:|x|
    Code:
                      |
          *           |           *
            *         |         *
              *       |       *
                *     |     *
                  *   |   *
                    * | *
         -------------*--------------
                      |

    The graph of: . y \:=\:|x+7| .is the previous graph moved 7 units to the left.
    Code:
        *                         | *
          *                       *
            *                   * |
              *               *   |
                *           *     |
                  *       *       |
                    *   *         |
       ---------------*-----------+------
                     -7           |

    The graph of: . y \:=\:4|x+7| .is the previous graph only "steeper".
    Code:
                                  |
                *           *     |
                 *         *      |
                  *       *       |
                   *     *        |
                    *   *         |
                     * *          |
          ------------*-----------+------
                     -7           |

    The graph of: y \:=\:-4|x+7| . is the previous graph reflected over the x-axis.
    Code:
                                  |
                     -7           |
          ------------*-----------+---- 
                     * *          |
                    *   *         |
                   *     *        |
                  *       *       |
                 *         *      |
                *           *     |
                                  |

    The graph of: y \:=\:-4|x+7| + 20 .is the previous graph raised 20 units.
    Code:
                              |
                      *       |
                     * *      |
                    *   *     |
                   *     *    |
                  *       *   |
          -------*---------*--+--------
                *           * |
               *             *|
              *               * 
             *                |*
            *                 | *
           *                  |  *
                              |

    You should be able to answer the questions now.

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