Vertex Form Parabola: Max and Min Dynamic Demo

This GeoGebra example dynamically demonstrates the vertex form of a quadratic function y = a(x-h)² + k, showing how parameters a, h, and k affect the parabola's shape, position, and its maximum or minimum value. The core mathematical concepts include the vertex form, axis of symmetry, direction of opening, and determination of extrema (maximum/minimum). Construction highlights: the Intersect command is used to find intersection points, while sliders or text objects (a, h, k, f, text1-text5, A, b) control parameters and display results, updating the graph and values in real time. Suitable for middle and high school mathematics teaching, this example helps students understand transformations of quadratic graphs and extremum problems, and can be used for classroom exploration or self-directed learning.