How do I Calculate Control Point/Handle X-Position for a Cubic Bezier Curve if I have the Formula?

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I have a curve that adheres to the bezier formula, and then I have to back-calculate the handle positions.

https://www.particleincell.com/2012/bezier-splines/

We know that the Po or Poy are [493.33970441 486.78826487 497.69599613 489.07543952] for Po, P1, P2, P3, through least squares interpolation. Now I need to find the handles Px positions.

P0 = (0, 493.33970441)
P1 = (P1x, 486.78826487)
P2 = (P2x, 497.69599613)
P3 = (1, 489.07543952)

I might not understand correctly, but I'd like to draw the position of where the handle is on the corresponding chart.

enter image description here

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