Practice!

Sample Problem

Find the standard form of the equation of a parabola (centered at the origin) with a directrix at y=-3 and a vertex at (0, 0).

Solution

The axis of this parabola is vertical, which means the directrix always takes the form y=k-p.

In this case, we know the directrix equation is y=-3=k-p=0-p (k=0 since we are at the origin)

y=-3=-p → p=3

The standard form of a parabola when centered at the origin is x2=4py, where h=0, k=0 and p=3

So, the equation is

x2=4(3)y=12y

x2=12y