Question

which translation maps the vertex of the graph of the function $f(x) = x^2$ onto the vertex of the function $g(x) = -8x + x^2 + 7$?
\bigcirc left 4, down 9
\bigcirc left 4, up 23
\bigcirc right 4, down 9
\bigcirc right 4, up 23

Explanation:

Step1: Find vertex of $f(x)=x^2$

The vertex of $f(x)=x^2$ is $(0,0)$.

Step2: Rewrite $g(x)$ in vertex form

Complete the square for $g(x)=x^2-8x+7$:

$$\begin{align*} g(x)&=x^2-8x+16-16+7\\ &=(x-4)^2-9 \end{align*}$$

Step3: Identify vertex of $g(x)$

From $g(x)=(x-4)^2-9$, the vertex is $(4,-9)$.

Step4: Determine translation

To go from $(0,0)$ to $(4,-9)$: shift right 4, down 9.

Answer:

right 4, down 9