Half-turn Symmetry: Quadratic Functions and Circle Transformations

This example demonstrates half-turn symmetry, where a figure coincides with itself after rotating 180 degrees around a center point. Core mathematical concepts include quadratic functions, circles, secant lines, and piecewise functions. Construction utilizes GeoGebra commands such as Point, Line, Segment, Midpoint, and Rotate to create objects like A, B, f, C, and their images A', C', h'. It is suitable for high school geometry or function graphing lessons to visualize symmetry properties.