Question

14.8.2 test (cst): conic sections the vertex of the parabola below is at the point (-4, -2). which of the equations below could be the one for this parabola? a. x = 2(y - 4)^2 - 2 b. y = -2(x - 4)^2 - 2 c. x = 2(y + 2)^2 + 4 d. x = -2(y + 2)^2 - 4

Explanation:

Step1: Recall parabola vertex - form

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

Step2: Identify the vertex values

Given the vertex $(h,k)=(-4,-2)$, so $h = - 4$ and $k=-2$.

Step3: Substitute into the formula

Substituting $h=-4$ and $k = - 2$ into the vertex - form $x=a(y - k)^2+h$, we get $x=a(y+2)^2-4$.

Step4: Check the options

Among the given options, when $a=-2$, the equation $x=-2(y + 2)^2-4$ matches the form of the horizontal parabola with vertex $(-4,-2)$.

Answer:

D. $x=-2(y + 2)^2-4$