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First, let's take a new view of our coordinate system:

standard coordinate system ... positive x's on the right, negative x's on the left, positive y's on top, and negative y's on bottom

We'll need to be thinking about these a lot to get through this!

Now, let me introduce you to Sideways Parabola Guy:

x = y^2 instead of y = x^2

graph of x = y^2 ... sideways parabola guy ... includes points ( 4 , 2 ) , ( 1 , 1 ) , ( 1 , -1 ) , ( 4 , -2 )

He's the same shape as Standard Parabola GuyHe opens towards positives -- just like Standard Parabola Guy:

standard parabola guy opens up towards positive y's

sideways parabola guy opens right towards positive x's

Now, we are going to need to be able to move this new guy around.  Let's look at what's happening a little at a time: