Draw curve through 3 points (not the control point)

I’m attempting to make a curve drawing tool a bit easier to use. Rather than drawing a basic curve and then clicking on the control point to change it, I would like the user to be able to click on the curve itself to change it, much as you do in the FlashIDE.

So, given start and end points, and a point on the curve, how do you determine the control point for use with the MX API?
(I googled this, but found mostly info on cubic rather than quadratic curves)