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 $g(x)$

The vertex of $g(x)$ is at $(6, 0)$.

Step2: Identify vertical stretch factor

The parabola has the same width as $f(x)=x^2$, so $a=1$.

Step3: Substitute into vertex form

Vertex form is $g(x)=a(x-h)^2+k$, where $(h,k)$ is the vertex. Substitute $a=1$, $h=6$, $k=0$.
$g(x)=1(x-6)^2+0$

Step4: Simplify the expression

$g(x)=(x-6)^2$

Answer:

$g(x)=(x-6)^2$