# How do I find the directrix of the parabola whose equation is y=x^2/32?

Oct 19, 2014

You have a parabola with vertex at $\left(0 , 0\right)$ that is opening upward.

That means your directrix is horizontal.

To get the directrix, transfer ${x}^{2}$'s coefficient to the other side.
Equate the resulting coefficient of $y$ to $4 d$, where $d$ is the distance from the vertex to the directrix

$y = {x}^{2} / 32$
$\implies 32 y = {x}^{2}$

$4 d = 32$
$\implies d = 8$

Since the parabola is opening upward, the directrix is below the vertex.

$y = h - d$

$y = 0 - 8$

$y = - 8$