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So far, we've only graphed lines...  But, there are tons of other things out there to graph.  ( I know.  This is all VERY exciting! )

Quadratics have graphs called "parabolas."

Here's our most basic quadratic:

 

y = x^2

He's also our most basic parabola.
I call him Standard Parabola Guy!

 

Before I show you his graph, let's understand what Standard Parabola Guy does for a living:

He squares things!

He's a squaring machine, baby!

Things go in...  and their squares spit out. 
We feed x guys into the machine...  and y guys spit out.

Let's feed the machine and this will give us the point to graph for Standard Parabola Guy...