I have three points (250, 0), (500,500) and (750, 0). To find a curve passing through these points all I have to do is plug-in these values into the general quadratic equation:
f(x) = ax^2 + bx + c
getting:
f(x) = -x^2/125 + 8x -1500
But, this is specific to this curve.
How would I generalize this to a curve that passes through (j, k), (p,q) and (u,v) such that the equation
f(x) = ax^2 + bx + c
has a, b and c expressed in terms of j,k,p,q,u and v; thus allowing me to plug-in arbitrary point values into this new general equation to get a specific equation for a curve?
I tried solving and eliminating variables, but all I end up with is an unsimplifiable mess that becomes too large to handle and I can't get very far.