Calculating control points

So I have these bezier/quad/whatever curves I want to make, and to make them, I need to know the control point(s).

Short of just picking random values until I come up with a curve that I like, is there some way of taking a curve and determining where/what its control points are (i.e. xy coordinates)? I am hoping there is a program in existence that can calculate that, but if not, a good tutorial would do.

Thanks a ton!