Problem
Writing an Equation in Vertex The parent function of the function $g(x)=(x-h)^{2}+k$ is $f(x)=x^{2}$. The vertex of the function $g(x)$ is located at $(9,-8)$. What are the values of $h$ and $k$ ? \[ g(x)=(x- \] \[ )^{2}+ \]
Solution
Step 1 ：The parent function of the function $g(x)=(x-h)^{2}+k$ is $f(x)=x^{2}$. The vertex of the function $g(x)$ is located at $(9,-8)$.
Step 2 ：The values of $h$ and $k$ are $h = 9$ and $k = -8$. Therefore, the function $g(x)$ can be written as $g(x) = (x-9)^2 - 8$.
Step 3 ：\(\boxed{g(x) = (x-9)^2 - 8}\)
