Quadratic Function Transformations Exploration

This GeoGebra example explores how the parameters a, h, and k transform the graph of a quadratic function y = a(x-h)² + k. Users can dynamically adjust each parameter to observe vertical/horizontal stretches, compressions, reflections across the x-axis, and horizontal/vertical translations of the parabola’s vertex. The construction leverages GeoGebra objects such as parent and Transformed functions, along with auxiliary objects like abs_h, abs_k, negneg, posneg, pospos, and negpos to manage sign combinations and coordinate tracking across different quadrants. Core mathematical concepts include quadratic function transformations, parameter effects on graph shape and position, and vertex geometry. Suitable for high school algebra and functions units, classroom demonstrations, or student-led investigations into function behavior.