Projectile Movement Between Two Points

Hey,

I have two points on the stage. I need to move a projectile from one point to the other with parabolic motion, reaching a certain maximum height. The known variables are, therefore, the (x,y) start coordinate, the (x,y) end coordinate, and the y coordinate of the vertex of the parabola. I’ve been trying for some time, but have been unable to find a flawless way to efficiently move the projectile between the two points. How would one go about doing this?

Thanks for your help!