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) = )

Explanation:

Step1: Identify vertex of $f(x)$

The vertex of $f(x)=x^2$ is $(0,0)$.

Step2: Identify vertex of $g(x)$

From the graph, vertex of $g(x)$ is $(-4,2)$.

Step3: Use vertex form formula

Vertex form is $g(x)=a(x-h)^2+k$, where $(h,k)$ is vertex, $a=1$ (no vertical stretch/compression). Substitute $h=-4$, $k=2$, $a=1$:
$g(x)=1(x-(-4))^2+2=(x+4)^2+2$

Answer:

$g(x)=(x+4)^2+2$