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 $(7, -8)$

Step2: Recall vertex form of parabola

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

Step3: Determine $a$ value

Since $g(x)$ is a translation of $f(x)=x^2$, $a=1$

Step4: Substitute values into vertex form

Substitute $a=1$, $h=7$, $k=-8$: $g(x)=(x-7)^2-8$

Answer:

$g(x)=(x-7)^2-8$