Question

the graph shows g(x), which is a translation of $f(x) = x^{2}$. write the function rule for g(x).
write your answer in the form $a(x - h)^{2} + k$, where a, h, and k are integers or simplified fractions.
$g(x) = \square$

Explanation:

Step1: Identify vertex of $g(x)$

The vertex of $g(x)$ is at $(9, 0)$ from the graph.

Step2: Recall vertex form of parabola

The vertex form is $g(x)=a(x-h)^2+k$, where $(h,k)$ is the vertex. Here $h=9$, $k=0$.

Step3: Determine stretch factor $a$

Since $g(x)$ is a translation of $f(x)=x^2$, there is no vertical stretch/compression, so $a=1$.

Step4: Substitute values into vertex form

Substitute $a=1$, $h=9$, $k=0$ into the formula.
$g(x)=1(x-9)^2+0$
Simplify to get the final function.

Answer:

$g(x)=(x-9)^2$