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 is $(-1, 0)$

Step2: Recall vertex form

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

Step3: Substitute vertex values

Substitute $h=-1$, $k=0$: $g(x)=a(x-(-1))^2+0=a(x+1)^2$

Step4: Find $a$ using a point

Use $(0,1)$: $1=a(0+1)^2 \implies a=1$

Step5: Write final function

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

Answer:

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