Control loop for finding maximum value
I'm assuming X starts at zero or full-scale.

Set X to ramp at a predetermined rate and look at the rate of change in Y  with respect to time - when it starts to approach zero, reduce X's rate and recalc the now-much-slower rate of change of Y as it approaches the peak.

I suspect that with a parabola, that if any two points measured in Y with respect to X you can make a near instant computation to predict the peak. Both points need to be on one side of the paraboa of course.

The noise on top of the parabola can be mitigated by a proper digital filter.