I have a parabola equation $y = ax^2 + bx + c$ with vertex at (vertexX, vertexY)) which draws the object's moving trajectory (from point $A(0;0)$ to $B(X;Y)$). Also, I have a gravity vector ($G(0;-g)$).

How to find the initial velocity which I should to set to this object to move it by this trajectory?

I tried the (vertexY / b, vertexY) but it is too small and doesn't depend on gravity.