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Math Help - function help please

  1. #1
    Newbie
    Joined
    Oct 2008
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    9

    function help please

    f(x)=1/4(x+2)^2-4.

    i) explain how the parabola that is the graph of f can be obtained from the graph of y=x^2 by using appropriate translations and scalings.

    ii) find the x-intercepts and y-intercept of the parabola.
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  2. #2
    Super Member

    Joined
    May 2006
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    Lexington, MA (USA)
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    Hello, toplad!

    f(x)\:=\:\tfrac{1}{4}(x+2)^2-4

    i) Explain how the graph of f(x) can be obtained from the graph of y\,=\,x^2
    by using appropriate translations and scalings.
    We know the graph of y \:=\:x^2
    Code:
                  |
           *      |      *
                  |
            *     |     *
             *    |    *
               *  |  *
          --------*--------
                  |

    The curve: y \:=\:(x+2)^2 is the previous graph moved 2 units to the left.
    Code:
                     |
           *         |   *
                     |
            *        |  *
             *       | *
               *     *
          --------*--+-----
                     |

    The curve: y \:=\:(x+2)^2-4 is the previous graph moved 4 units down.
    Code:
                     |
           *         |  *
                     |
          --*--------+-*--
             *       |*
               *     *
                  *  |
                     |

    The curve y \;=\;\tfrac{1}{4}(x+2)^2-4 "rises more slowly" . . . Hence, it is "wider".
    Code:
       *             |       *
                     |
        *            |      *
     ----*-----------+-----*----
           *         |   *
              *      |*
                  *  |
                     |
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