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.

Explanation:

Step1: Identify vertex of $g(x)$

The vertex of $g(x)$ is $(0, -1)$.

Step2: Recall vertex form formula

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

Step3: Substitute vertex values

Substitute $h=0$, $k=-1$, $a=1$ (no vertical stretch):
$g(x)=1(x-0)^2+(-1)$

Step4: Simplify the expression

$g(x)=x^2 - 1$

Answer:

$g(x)=x^2 - 1$