for a parabola the end point positions on Y dont matter.
the curve if from xa to xb using the solution for the equation ax^2 + bx + c
you need to solve three equations but I posted the code for that , or I can give you a python program that solves for 3 points. The hard part is getting the third point .

I never saw that way of splitting a tri to quads. That could be very useful.