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Ruler and compass on parabola and axis

Source: Tuymaada 2020 Senior, P5 (Junior, P5)

October 6, 2020
conicsparabolaconstructiongeometryalgebraanalytic geometryquadratics

Problem Statement

Coordinate axes (without any marks, with the same scale) and the graph of a quadratic trinomial y=x2+ax+by = x^2 + ax + b are drawn in the plane. The numbers aa and bb are not known. How to draw a unit segment using only ruler and compass?
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