Quadratic Function Rotation: Square and Cosine Transformations

This GeoGebra example demonstrates how to apply rotation and translation transformations to quadratic function graphs while exploring their geometric properties using squares and cosine functions. Core mathematical concepts include the relationship between quadratic function equations and their graphs, coordinate calculations for rotation transformations, and the periodicity and symmetry of cosine functions. Construction details: uses parameters a and c to control function coefficients, applies rotate and translate commands for image transformations, constructs auxiliary squares with cosine functions, and displays dynamic calculation results via text1. Suitable for high school mathematics lessons on functions and trigonometry, demonstrating how parameter changes affect function graphs and helping students intuitively understand the geometric meaning of translation and rotation formulas. Can also serve as exploration material for combining coordinate geometry with algebra.