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).