Thread: 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.

Hello, toplad!

i) Explain how the graph of can be obtained from the graph of
by using appropriate translations and scalings.

We know the graph of

Code:

              |
       *      |      *
              |
        *     |     *
         *    |    *
           *  |  *
      --------*--------
              |

The curve: is the previous graph moved 2 units to the left.

Code:

                 |
       *         |   *
                 |
        *        |  *
         *       | *
           *     *
      --------*--+-----
                 |

The curve: is the previous graph moved 4 units down.

Code:

                 |
       *         |  *
                 |
      --*--------+-*--
         *       |*
           *     *
              *  |
                 |

The curve "rises more slowly" . . . Hence, it is "wider".

Code:

   *             |       *
                 |
    *            |      *
 ----*-----------+-----*----
       *         |   *
          *      |*
              *  |
                 |