Non-rigid Transformations of Quadratic Functions: Exploring Vertex Form Graphs w

This GeoGebra example demonstrates how the graph of a quadratic equation in vertex form, y = a(x-h)² + k, transforms when the values of a, h, and k are changed using interactive sliders. Students can visually discover non-rigid transformations of the parabola, including vertical stretching and compressing, reflection across the x-axis, and horizontal and vertical translations. The core mathematical concepts involved are quadratic functions, parabolas, vertex form, function transformations, and coordinate geometry. The construction relies on GeoGebra objects c, h, k, a, text1, and d, where sliders drive dynamic updates to the function graph and accompanying text annotations. This resource is suitable for middle school and high school mathematics instruction, inquiry-based learning, and classroom demonstrations of graphing and transformation principles.