• Nov 17th 2008, 03:16 AM
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.
• Nov 17th 2008, 07:58 AM
Soroban

Quote:

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

i) Explain how the graph of \$\displaystyle f(x)\$ can be obtained from the graph of \$\displaystyle y\,=\,x^2\$
by using appropriate translations and scalings.

We know the graph of \$\displaystyle y \:=\:x^2\$
Code:

```              |       *      |      *               |         *    |    *         *    |    *           *  |  *       --------*--------               |```

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

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

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

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

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

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