Graphing Parabolas in Vertex Form with Interactive Parameters

This GeoGebra example demonstrates how to graph a parabola in vertex form by entering the vertex coordinates and four additional points to construct the quadratic function graph interactively. Core mathematical concepts include the vertex form of a quadratic function y = a(x − h)² + k, the vertex (h, k), axis of symmetry, opening direction, vertical stretch/compression governed by parameter a, and the algebraic-geometric correspondence between points and the function graph. The construction uses GeoGebra commands such as Textfield, If, and Sum, together with objects including a, h, k, f, a₁, h₁, k₁, InputBox1 through InputBox10, points A, B, C, D, E, lists list1 and list2, and button1. Text fields and input boxes enable real-time parameter adjustment, while conditional logic and summation control point generation and graph display. Suitable for middle and high school mathematics instruction, classroom demonstrations, student-centered exploration, and visualization practice of parabola translation and scaling.