Transformation of Quadratics: Shifts, Stretches, and Reflections

This GeoGebra example demonstrates how quadratic functions transform under parameter changes, including horizontal/vertical translations, vertical stretches/compressions, and reflections. The core mathematical concepts involve the standard and vertex forms of quadratics, the effects of coefficients on the vertex, axis of symmetry, and roots, as well as the geometric interpretation of function transformations. Construction highlights: the base function f is defined as a quadratic, sliders a and b control transformation parameters, and text objects text1 and text2 dynamically display the current equation and key features; the transformed function g updates in real time. This resource is ideal for middle and high school mathematics, supporting lessons on functions, transformations, and graphing, and encourages exploratory learning to connect algebraic parameters with visual graph changes.