Find the equation of the parabola w/ v(3,-4) and with directrix y=0.

Answer 1

Since the distance from the vertex to the directrix is 4, then the standard parabola

x^2 = 4py

has p=4. So, with the translation of the vertex to (3,-4), and the directrix above the vertex, the parabola opens downward, so the equation is

(x-3)^2 = -16(y+4)

confirmed at

http://www.wolframalpha.com/input/?i=parabola+(x-3)%5E2+%3D+-16(y%2B4)

You may, of course massage that equation into the form desired.