Question

the graph shows g(x), which is a translation of f(x) = x². 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) =

Explanation:

Step1: Identify vertex of $g(x)$

Vertex is $(-5, 7)$

Step2: Recall vertex form of parabola

Vertex form: $g(x)=a(x-h)^2+k$ where $(h,k)$ is vertex

Step3: Substitute vertex values

Substitute $h=-5$, $k=7$, $a=1$ (no vertical stretch/compression):
$g(x)=1(x-(-5))^2+7$

Step4: Simplify the expression

$g(x)=(x+5)^2+7$

Answer:

$g(x)=(x+5)^2+7$