Solving Quadratic Equations: Discriminant, Roots, and Graph Visualization

① This GeoGebra example dynamically demonstrates the process of solving a quadratic equation ax²+bx+c=0, closely linking algebraic solutions with the parabolic graph and showing how the discriminant affects the nature of the roots. ② Core mathematical concepts include quadratic equations, the discriminant, the quadratic formula, the axis of symmetry and vertex of a parabola, and the correspondence between roots and x-intercepts of the graph. ③ Construction highlights: using the Polynomial command to define the quadratic function, OrthogonalLine and Point to create auxiliary geometric elements, with sliders or objects a, b, c as adjustable parameters; it computes the discriminant disc and roots root1 and root2, and generates multiple text objects (text1 to text9) to dynamically display the equation and solutions, along with coefficient objects (constant, linear, quad), a scale factor, and auxiliary points F, G, D, E, H, I. ④ Suitable for middle and high school mathematics (grades 8–12) to study the relationship between quadratic equations and their graphs, and for teachers to use in classroom demonstrations or for students to explore how changing parameters affects the roots.