Roots of a Parabola: Interactive Exploration

① This GeoGebra example dynamically visualizes the roots (x-intercepts) of a parabola y = ax² + bx + c as the coefficients change, helping learners understand the relationship between quadratic equations and their graphs. ② Core mathematical concepts include quadratic functions, roots/zeros of a parabola, the discriminant, intersections with the x-axis, and how parameter variations affect the solutions. ③ Construction highlights: the Intersect command is used to find the parabola's intersection points with the x-axis; sliders (a, b, c) control the coefficients; text objects (text1 through text10) dynamically display root values and discriminant information; involved objects include the curve, points A and B, and auxiliary elements α, β, s, p, o, r. ④ Suitable for middle and high school students learning quadratic functions and equations, as well as for classroom demonstrations or self-study, allowing users to adjust coefficients and observe how roots change, deepening understanding of the discriminant and root properties.