How to know initial jumping velocity if I know trajectory as parabola equation and gravity value? 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.
 A: Let initial velocity be $(u_x,u_y)$
differentiating the parabolic equation w.r.t. x gives $\frac{dy}{dx} = b$ when $x=0$
so $$\frac{u_y}{u_x} = b$$
Also from the equations of motion horizontally and vertically using time $t$ to be the time to the vertex $(X,Y)$
$$t=\frac{X}{u_x}$$
$$Y = u_yt -\frac{gt^2}{2}$$
solving these three brings us to a suggestion for your initial velocity of
$$u_x = X(\frac{2}{g}(bX-Y))^{-0.5}$$
and $$u_y = bu_x$$
hope that works...
A: First you have $x(0)=y(0)=0$. $v_y/0)/v_x(0)=b$, second  you have $v_y(vertex)=0, 
 and , v_y(t)=v_y(0)-g*t ,  y(vertex)=v_y(0)*t-g/2*t^2,  x(t)=v_x(0)*t$
this should be enough to find a,b,c
A: This formula gives approximately correct result (but with longer time than I put to formula):
Velocity = FVector(
((vertY / Props.JumpTime) + (0.5f * -GravityZ * Props.JumpTime)) / b,
0.0f,
(vertY / Props.JumpTime) + (0.5f * -GravityZ * Props.JumpTime)
);
VertY - the Y of highest point of parabola
GravityZ - gravity magnitude
Props.JumpTime - time for moving
