Question

Write an equation for the parabola with vertex (–2, 4) and focus (–2, 1).

Answer 1

since the focus is 3 vertical units away from the focus, a=-3. so the equation is (x+2)^2=-12(y-4)
this is in vertex form: (x-h)^2=4(a)(y-k)

Answer 2

where (h,k) is your vertex.

Answer 3

so is it y=1/12(x-2)^2-4

Answer 4

if you want y explicitly, solve for y:
(x+2)^2=-12(y-4)
(x+2)^2=-12y+48
-12y=(x+2)^2+48
y=(-1/12)*(x+2)^2-4