Hi, is it possible to find the (best fit) equation of a/any Parabola given *two* points and the following additional constraints:
i) The Axis is parallel to the y-axis ( vertical )
ii) The Axis lies between the two points
iii) The vertex is higher than both points
iv) The vertex is a maxima, or the Parabola opens downwards.
v) One point can be the origin.
This is basically for the path of a projectile under gravity that originates from a start point and must hit a target point, following a parabolic path.
So for the equation: y = a(x - b)^2 + c, I understand that I need three equations to solve all constants, which normally requires three points.
Is it possible to find ( or approximate ) the third equation given the above constraints somehow?
Is there possibly a (simple'ish) iterative technique? ( Unfortunately speed is a factor as this is part of program's run-time algorithm ).
Many thanks for any help!