Vertex Form for Quadratic Functions: Dynamic Parameter Exploration

① This example dynamically demonstrates how the vertex form of a quadratic function, f(x)=a(x-h)²+k, changes its graph as parameters a, h, and k are varied, showing the vertex location, opening direction, and width. ② Core mathematical concepts include the vertex form of quadratic functions, the roles of parameters a (vertical stretch/reflection), h (horizontal shift), and k (vertical shift), and transformations of parabolas. ③ Construction highlights: using GeoGebra, the function f is defined with sliders for a, h, and k; a text object text1 displays the current equation; an auxiliary object g (possibly a line or axis) helps visualize the vertex and symmetry. ④ Suitable for middle-to-high school students learning quadratic functions, and useful for teachers as an interactive demonstration or for students to explore parameter effects independently.