f( x ) = -x^2up-side-down Standard Parabola Guy
We've got one mountain.


The tails both shoot down.

Parabolas can also cross the x-axis TWO times (since their degree is TWO.)  This happens when they have extra terms (other stuff added on!)

Likef( x ) = x^2 - 4
Standard Parabola Guy shifted down 4

Fourth degree polynomials get a lot more exciting...  If they have extra stuff added on.

f( x ) = x^4is pretty boring.  If you grab a graphing
calculator* to graph him, you'll see that he looks a lot like Standard Parabola Guy - but with a wider valley.

wider here
wider Standard Parabola Guy
Still, the tails
both shoot up.