calculating parameters for defining subsections of quadratic bezier curves

Question

I have a quadratic bezier curve described as (startX, startY) to (anchorX, anchorY) and using a control point (controlX, controlY).

I have two questions:

(1)

Answer 1

The t equation is wrong, you need to use eq(1)

(1) x = (ax-2bx+cx)t2+2(bx-ax)t + ax

and solve it using the the quadratic formula for the roots (2).

           -b ± √(b^2 - 4ac)
  (2)  x = -----------------
              2a

Where

a = ax-2bx+cx
b = 2(bx-ax)
c = ax - x