Question

which equation has a graph that is a parabola with a vertex at (-2, 0)? y = x² - 2; y = (x - 2)²; y = (x + 2)²; y = -2x²

Explanation:

Step1: Recall vertex form of parabola

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

Step2: Substitute vertex $(-2,0)$

Substitute $h=-2$, $k=0$ into the vertex form:
$y = (x - (-2))^2 + 0 = (x + 2)^2$

Step3: Verify other options (optional check)

• For $y=x^2-2$, vertex is $(0,-2)$
• For $y=(x-2)^2$, vertex is $(2,0)$
• For $y=-2x^2$, vertex is $(0,0)$

Answer:

$\boldsymbol{y=(x+2)^2}$