Solving Quadratic Equations Graphically & Symbolically

① This example dynamically demonstrates the solution of quadratic equations ax²+bx+c=0 by combining graphical visualization with symbolic computation, showing the discriminant, roots, and the intersection of the parabola with the x-axis. ② Core mathematical concepts include quadratic functions, quadratic equations, the discriminant, the quadratic formula, vertex and axis of symmetry, and the correspondence between graphical and algebraic representations. ③ Construction highlights: using GeoGebra commands such as OrthogonalLine to create perpendicular lines, Point to define key points, and Polynomial to generate polynomial functions; objects include coefficients a, b, c, discriminant disc, roots root1 and root2, the parabola f, and line g, with sliders or inputs to adjust coefficients in real time, updating both the graph and symbolic results. ④ Suitable for middle and high school algebra and function lessons, as well as pre-calculus review, helping students understand the geometric meaning of quadratic solutions and their algebraic derivation.