Quadratic Function Graph and Its Roots

This GeoGebra example demonstrates the geometric relationship between the graph of a quadratic function (a parabola) and its roots, showing that the roots correspond to the intersection points of the parabola with the x-axis. Core mathematical concepts include quadratic functions, parabolas, function zeros/roots, the discriminant and number of real roots, and coordinate geometry. The construction uses the GeoGebra Intersect command on objects a, b, c, f, A, B, Text1, d, Text2, and Text4 to compute intersections between the function graph f and relevant lines, labeling the resulting points A and B as roots with explanatory text. It is suitable for middle school and high school algebra and analytic geometry courses, as well as self-study of quadratic function properties and the geometric meaning of roots.