Summer of Math Exposition

Why is y = (x - 3)² to the RIGHT of y = x²? There's a lot of different ways to explain this, but the way I prefer to explain it doesn't seem all that common on the internet. In my entry for SoME3, I provide a explanation that revolves around the relationship between a pre-transformation point and a post-transformation point. I then show how you could use this thinking to tackle two standard types of function transformation math problems.