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 $k$ ?
\[
g(x)=(x-
\]
\[
)^{2}+
\]

Answer

Expert–verified

Hide Steps

Answer

$\boxed{g(x) = (x-9)^2 - 8}$

Steps

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 ：$\boxed{g(x) = (x-9)^2 - 8}$