Explain what each of the following represents, and how equations (a) and (b) are equivalent.

Question

(a) y = a(x - h)2 + k, a ≠ 0
(b) (x - h)2 = 4p(y - k), p ≠ 0
(c) (y - k)2 = 4p(x - h), p ≠ 0

can you check my work and explain how equations (a) and (b) are equivalent.

(b)This equation is used when the parabola has a vertical axis. In this equation (h,k) represents the vertex, (h, k+p) represents the focus, and (y=k-p) represents the directrix. The axis is the line x=h. When p>0 the parabola opens upward and when p<0 it opens downward.
(c) This equation is used when the parabola has a horizontal axis. In this equation (h,k) represents the vertex,( h+p,k)represents the focus, and (x=h-p) represents the directrix. The axis line is the line y=k. When p>0 the parabola opens to the right and when p<0 it opens to the left.

Answer 1

(a) and (b) are equivalent, since you can write them as

(y-k) = a(x-h)^2
(y-k) = 4p(x-h)^2

You have (b) and (c) right.

I thought we already went over this...