How do I find the vertex, focus, and directrix of a parabola?

Arrange your equation in this form:

(x-h)^2=4p(y-k)

or

(y-k)^2=4p(x-h)

The vertex is (x,k); the focus is (h, k+p); the directrix is y=k-p where p is the distance from the vertex to the focus.

You can also search;

Parabola - Wikipedia, the free encyclopedia

Basically, you put your equation into a general form.

\left(x-h^2\right)=4p\left(y-k\right) \text { axis parallel to the Y-axis}

or

\left(y-k^2\right)=4p\left(x-h\right) \text{ axis parallel to the X-axis}

vertex = (h,k)
focus = (h,k + p)
directrix y = k − p. p is the distance from the vertex to the focus


Link to: Parabola - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Parabola)