Algebra II : Find the standard form equation of the parabola with vertex (0,0) and directrix x= 9/2. Can someone please explain how to solve this one? (and solve. We got the answer, x=-18y^2, I just want to make sure its right.

Question

Algebra II :  Find the standard form equation of the parabola with vertex (0,0) and directrix x= 9/2. Can someone please explain how to solve this one? (and solve. We got the answer, x=-18y^2, I just want to make sure its right.

whpalmer4 · Answer

Mmm...the directrix isn't right...

whpalmer4 · Answer

The vertex form equation for a parabola with a horizontal axis of symmetry and vertex at $(h,k)$ is $$(y-k)^2=4p(x-h)$$$p$ is the distance from vertex to focus and vertex to directrix.  Our vertex is at $(0,0)$ so that becomes$$y^2=4px$$$$p=0-\frac{9}{2} = -\frac{9}{2}$$so we have$$y^2=4(-\frac{9}{2})x$$$$ y^2=-18x$$

A plot of the parabola is attached.