Question

graph the parabola:
$f(x)=2(x - 3)^2 - 2$

Explanation:

Step1: Identify vertex form

The function is in vertex form $f(x)=a(x-h)^2+k$, where $(h,k)$ is the vertex. For $f(x)=2(x-3)^2-2$, $h=3$, $k=-2$, so vertex is $(3,-2)$.

Step2: Determine parabola direction

Since $a=2>0$, the parabola opens upward.

Step3: Verify key points

Calculate $f(2)=2(2-3)^2-2=0$, $f(4)=2(4-3)^2-2=0$, so the parabola passes through $(2,0)$ and $(4,0)$.

Answer:

The correct graph is the second one (the middle-top graph with vertex at $(3,-2)$, opening upward, passing through $(2,0)$ and $(4,0)$).