Parabola Parameter Transformation

This GeoGebra example dynamically explores how the parameters a, h, and k in the quadratic function y = a(x−h)² + k affect the parabola’s vertex, direction, width, and position. It illustrates core concepts of function transformations, including vertical/horizontal stretches, compressions, and translations, expressed in vertex form. Construction utilizes GeoGebra objects such as parameters a, h, k, the function f, and text labels text1–text3 to enable real-time slider-based interaction. The model is suitable for high school algebra and pre-calculus students learning function behavior, as well as teachers designing interactive lessons on quadratic transformations.