Question

select the correct answer.
the graph of a function is a parabola that has a minimum at the point (-3,9). which equation could represent the function?
a. $g(x)=2(x + 3)^2 + 9$
b. $g(x)=-\frac{1}{2}(x - 3)^2 + 9$
c. $g(x)=3(x - 3)^2 + 9$
d. $g(x)=-(x + 3)^2 + 9$

Explanation:

Step1: Recall vertex form of parabola

The vertex form of a parabola is $g(x)=a(x-h)^2+k$, where $(h,k)$ is the vertex.

Step2: Match vertex values

The vertex is $(-3,9)$, so $h=-3$, $k=9$. Substitute into the formula: $g(x)=a(x-(-3))^2+9=a(x+3)^2+9$.

Step3: Check for minimum

A parabola has a minimum when $a>0$ (opens upward).

Step4: Identify valid option

Only option A has $a=2>0$ and matches $g(x)=a(x+3)^2+9$.

Answer:

A. $g(x)=2(x + 3)^2 + 9$