Ok, lets say you start at (0,0) at time t=0.
That means your coordinates while "holding the jump button" are:
$$x(t<t_0) = v_x * t$$ $$y(t<t_0) = v_y * t$$
(with $v_x <= 220$ and $v_y = 600$)
Your coordinates when releasing the jump-button at time $t=t_0$ are therefore $$(v_xt_0, v_yt_0)$$ Thats where your parabola starts with $$x(t>t_0) = v_x * (t-t_0) + v_x * t_0 = v_xt$$ $$y(t>t_0) = -g/2 * (t-t_0)^2 + v_y (t-t_0) + v_yt_0 = -g/2 * (t-t_0)^2 + v_y*t$$
(with $g=2100$) Note that your x-position is totally unaffected by $t_0$ and your y-position is somewhat like an unaffected linear movement in y-direction plus an affected acceleration in negative y-direction. (Ignore the physical inaccuracy in this sentence!)
In these equations we have 2 parameters to choose: $v_x$ (in a limit) and $t_0$ (probably also in a limit). So given some target position $(X>0,Y>0)$ how do you choose those to get to that position as fast as possible?
The arrival time is $t_a=X/v_x$ and our y-position at that time is $$Y = y(t_a) = -g/2 * (t_a-t_0)^2 + v_xt_a$$ $$Y = -g/2 * (X/v_x-t_0)^2 + v_yX/v_x$$ $$0 = -g/2t_0^2 + \frac{gX}{v_x} t_0-\frac{gX^2}{2v_x^2} + X\frac{v_y}{v_x} - Y$$ $$0 = t_0^2 - \frac{2X}{v_x} t_0+\frac{X^2}{v_x^2} - X\frac{2v_y}{gv_x} + \frac{2Y}{g}$$
Uhh, <PERSON>, pq-formula :-) $$t_0=\frac{X}{v_x}\pm \sqrt{\frac{X^2}{v_x^2}-\frac{X^2}{v_x^2} + X\frac{2v_y}{gv_x} - \frac{2Y}{g}}$$ $$t_0=\frac{X}{v_x}\pm \sqrt{X\frac{2v_y}{gv_x} - \frac{2Y}{g}}$$
Since you are probably not interested in the solution "Hold your jump button incredibly long and then go backwards through the parabola" you should be able to use just a $+$ instead of $\pm$.
You will also see, that this formula only produces real solutions if $$X\frac{2v_y}{gv_x} - \frac{2*Y}{g}>0$$ $$X\frac{v_y}{v_x} > Y$$ which is the condition that your linear part at the beginning must be steep enough to hit the target point. This might limit $v_x$.
So what you should do:
1. Check if the condition limits $v_x$. 563
If not, go as fast as possible.
2. Calculate $t_0$ with the formula above.
3. If you have a limit for $t_0$, check it. If your calculated result is higher, the jump is not possible.
4. Run, aim, JUMP (oh, and pray not to fall into the spikes) 229