I can't say I've ever used the "Equation Driven Curve" feature before now. I just tried it out, hoping to be able to use combinations of signum (step) functions to accomplish something piecewise. It didn't quite work out, SolidWorks seems to be able to process sgn(n) where n is a constant, but it wont do sgn(x), with x being a variable.
Also, I wasn't able to link any global variables in the Equation Driven Curve, so that seems quite problematic to your situation.
Since your equations are both 2nd order polynomials, why don't you try using two parabolas for your profile. That way you can control the shape by using Smart Dimensions (which CAN link to your global variables). For instance, dimension the point that they meet as y = m.
Just to add on to my answer, it seems like the second equation should have some dependence on "c", such that you would want y = 0 at x = c. I would change that to y = m / (c-p)^2 * [ (c^2 - 2pc) + 2px - x^2 ]