Dynamic Exploration of Parabola Translations and Dilations

This interactive GeoGebra example demonstrates how a parabola (quadratic function) changes under translations and dilations. The core mathematical concept is the quadratic function y=a(x-h)^2+k, where parameter a controls the opening direction and vertical stretch/compression, h controls horizontal shift, and k controls vertical shift. The construction uses DynamicCoordinates and If commands to compute key points dynamically, along with Point and Segment objects to create draggable control points (e.g., vertex and dilation handles). Sliders such as bH, bV, and vdilate allow real-time parameter adjustment. Objects include points A, B, C, P, Q, and text labels text1-text5 that display the current function expression. This resource is suitable for middle and high school students learning quadratic function transformations, and for teachers demonstrating the effect of parameters on the graph in classroom settings.