First I am assuming that the only force acting on the ball is gravity. If that is the cases then the ball flies in the form of a parabola.
So a parabola can be written in the form
Now from the problem we know that it must pass through these three points (if we put the origin at the launch point)
Plugging these ordered pairs into the equation gives a system of 3 equations in three unknows.
If you solve this you will have the equation of the parabola.