Quadratic Functions Transformations: Effects of a, h, k

This GeoGebra example demonstrates how the parameters a, h, and k in the vertex form of a quadratic function y = a(x-h)² + k affect the graph of a parabola. It visually shows vertical stretching/compression and reflection (via a), horizontal translation (via h), and vertical translation (via k). The construction uses three slider objects (a, h, k) and a quadratic function expression, allowing users to drag sliders and observe real-time changes in the parabola's vertex, axis of symmetry, and opening direction. This interactive tool is ideal for middle school to high school students learning function transformations, and serves as a powerful classroom demonstration or self-study resource to build intuition about parameter-image relationships.