10.1: Parabolas

To find the vertex, focus, and the directrix of a parabola, the equation of the parabola will have to be in standard form. 

The standard form of a parabolic equations is:

Often, to find the standard form, you need to complete the square. 

The vertex is (h, k) 

The focus is p units from the vertex. 

When p>0 and the x is squared, then add p to the y value. 

When p<0 and the x is squared, then subtract p from the y value. 

When p>0 and the y is squared, then add p to the x value. 

When p<0 and the y is squared, the subtract p from the x value. 

When the parabola is vertical, the directrix is y=k-p

When the parabola is horizontal, the directrix is x=h-p

Math joke of the day:

Q: Why couldn't the Möbius strip enroll at the school?

A: they required an orientation.