Determine the vertex form of the equation of a parabola with focus (-2,-4) and directrix y=-6

Question

anonymous · Answer

I've been working on this question for an hour and I can't figure it out..

tkhunny · Answer

Have you considered the definition?

Parabola: Locus of Points Equidistant from a given point (focus) and a given line (directrix).

What is the distance of any point from (-2,-4)?

$\sqrt{(x+2)^{2}+(y+4)^{2}}$

What is the distance of any point from y = -6

$|y+6|$

Where are they the same?

$\sqrt{(x+2)^{2}+(y+4)^{2}} = |y+6|$

Everything is positive, so square both sides and use your best algebra.

anonymous · Answer

the vertex is half way between the focus and the directrix, can you find what this point would be?
|dw:1397595103058:dw|