Rotating f(x)

I don't know if this is really that interesting but it just occurred to me that if you have some function, let's call it f(q).

You can do the following to make a parameterized curve of this parabola rotated any angle. 

here the parabola is rotated by 45 degrees clockwise. There are different operation to scale the function, or skew it or flip it various ways and a lot of functions are related visually that way.