Getting Bezier Handles from a Curve's control points

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I am working with a program that defines its Curves with 'Edges' that have three control points (The red points 0, 1, 2 in the attached image). I believe this is a Quadratic Curve.

This is a list of their x & y coordinates: [(736,620), (963, 488), (1200, 620)]. Point 1 determines the curvature of the 'Edge.'

I am trying to derive a Cubic Curve from this Quadratic Curve, then getting the X & Y of Handle 1 & 2. How may I go about this? Thank you.

Control Points

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