Alex S. answered • 12/02/20

Stanford Undergrad tutoring Math, Physics, and Languages

Hi Paul!

I believe this question is testing knowledge of the "vertex form of a parabola".

The vertex form of the parabola is where the equation for for a parabola is written as

y = a(x - h)^{2} + k.

The vertex of the parabola written in this way will always be at the point (h,k).

Looking at your equation y + 1 = 1/16(x - 2)^{2}, we almost have it in the right form. All we have to do is subtract one from both sides, which gives us

y = 1/16(x - 2)^{2} - 1.

Now your equation is written in vertex form, and we know that the vertex is at the point (h,k). What are h and k for your equation? Well h has to be 2, and k has to be -1. Therefore, the vertex of the parabola is at the point (2,-1).

Paul S.

Thank youuuu12/02/20