First, let's take a new view of our coordinate system:
We'll need to be thinking about these a lot to get through this!
Now, let me introduce you to Sideways Parabola Guy:
He's the same shape as Standard Parabola Guy. He opens towards positives -- just like Standard Parabola Guy:
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: