Question

Using the following information for the Vertex and Directrix, write the standard form equation for the parabola with what is given below.


Vertex: (-2,1)
Directrix: x=1

Answer 1

The horizontal parabola
y^2 = 4px has directrix p units from the vertex. So, since our directrix is 3 units from the vertex, we start with

y^2 = 12x

But, that's with a vertex of (0,0). So, our parabola is

(y-1)^2 = 12(x+2)

But, that opens to the right. Our vertex is to the left of the directrix, so we wind up with

(y-1)^2 = -12(x+2)

Verify that at

http://www.wolframalpha.com/input/?i=parabola+%28y-1%29%5E2+%3D+-12%28x%2B2%29