Question

find the equation for a parabola with it's focus at (0,3) and a directrix at y = -3

Answer 1

|a| = 1/(4p)
f(x) = a(x - h)^2 + k
Plug in the numbers. p is the focal distance.
a = 1/(4(3))
a = 1/12
f(x) = 1/12(x - h)^2 + k
Since the focus is at (0, 3) and the directrix at y = -3, there is no phase shift or vertical shift, so h and k and disappear.
f(x) = 1/12x^2