I like to call the graphs of polynomials "roller coaster graphs."  You'll see!

Let's get started:

Our easiest even degree polynomial is Standard Parabola Guy:

f ( x ) = x^2

graph of f ( x ) = x^2

Notice that both tails shoot off in the same direction -- up!

But, for what we are doing, this guy is kind of boring.

What if we shift him down?

f ( x ) = x^2 - 4

Notice that this guy crosses the
2 times... 
and his degree is
2 !


graph of f ( x ) = x^2 - 4