Question

14.8.2 test (cst): conic sections the vertex of the parabola below is at the point (-3, -5). which of the equations below could be the one for this parabola? a. y=(x + 3)^2 - 5 b. y=(x - 5)^2+3 c. y=(x + 3)^2+5 d. x=-3(y + 5)^2

Explanation:

Step1: Recall vertex - form of parabola

The vertex - form of a parabola that opens up or down is $y=a(x - h)^2+k$, where $(h,k)$ is the vertex of the parabola.

Step2: Identify the vertex values

Given the vertex $(h,k)=(-3,-5)$, so $h = - 3$ and $k=-5$.

Step3: Substitute into the vertex - form

Substituting $h=-3$ and $k = - 5$ into $y=a(x - h)^2+k$, we get $y=a(x+3)^2-5$. When $a = 1$, the equation is $y=(x + 3)^2-5$.

Answer:

A. $y=(x + 3)^2-5$