# Trying to find equation for parabola

• Jan 28th 2013, 09:30 AM
togo
Trying to find equation for parabola
Vertex of 0,3
Focus of 0,0
Formula for parabola:
y = a(x - h)^2 + k

I assume that h = 0, k = 3 (the vertex)
how does the focus factor into this equation? thanks.
• Jan 28th 2013, 11:38 AM
HallsofIvy
Re: Trying to find equation for parabola
Quote:

Originally Posted by togo
Vertex of 0,3
Focus of 0,0
Formula for parabola:
y = a(x - h)^2 + k

I assume that h = 0, k = 3 (the vertex)
how does the focus factor into this equation? thanks.

If you write the eqation of a parabola as $y= a(x- x_0)^2+ y_0^2$, the same as your formula with [itex]h= x_0[/itex], [itex]k= y_0[/tex], where [itex](x_0, y_0)[/itex] is the vertex, then the focal length is f= 1/4a.Parabola - Wikipedia, the free encyclopedia

Saying that the vertex is at (0, 3) and the focus is at (0, 0) means that the focal length is f=1/4a= 3 so that 4a= 1/3, a= 1/12. Of course, because the focus is below the vertex, the parabola opens downward, so a is negative.