Quadratic Function Graph with Roots and Vertex

① This GeoGebra example dynamically plots a quadratic function based on given parameters and highlights its roots (x-intercepts). ② Core mathematical concepts include the standard form of a quadratic, completing the square, vertex (extremum), factorization, and the geometric meaning of roots as intersections with the x-axis. ③ Construction details: uses commands such as CompleteSquare to convert to vertex form, Extremum to find the vertex, Root to compute roots, Factors for factorization, and Polygon/Corner to build a control panel and frame; sliders for parameters a and c allow real-time adjustment, while text objects display the roots, vertex, and factored form. ④ Suitable for middle and high school mathematics, this example helps students understand quadratic properties, graph transformations, root-finding methods, and the technique of completing the square, and serves as an interactive classroom demonstration or self-study tool.