u/Flugogrejs

I would like to find a quadratic function given p1, p2 and L.

L = c1 + c2

The y value of p3 is as low as possible. You could think of holding a string with length L at p1 and p2, and pulling it down.

The parabola is going to pass through all three points.

My intuition tells me this would be possible, but I may be wrong.

Please ask me questions if I haven't defined the problem enough.