Let p be an even-degree polynomial such that has a unique vertex (single global extremum). Consider the counterclockwise rotation of the 2d curve, which represents the polynomial graph in the Oxz plane, around the vertical axis that passes through the vertex by an angle θ (see figures below).
Given the x-value of a point P, xP, belonging to the 2d curve, find R being the rotated point P.
Hint. Find critical points for their identification and behavior.
input: (p, xP, theta)
output: R
Original 2d curve Rotating 3d
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Last Solution submitted on Feb 15, 2026

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George Berken

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