Quadratic Function and Tangent Intersection Dynamics

This GeoGebra example demonstrates the construction of a tangent line at any point on a quadratic function graph and the relationship between its intersections with coordinate axes. Using the Intersect command, it dynamically displays the quadratic function y=ax²+bx+c, its tangent line at point A, and shows how the intersection points with x-axis and y-axis change. Core mathematical concepts include quadratic function properties, tangent slope (geometric meaning of derivative), and solving line-axis intersections. Construction highlights: control quadratic function coefficients via parameters a, h, k, d, use Intersect command to find tangent-axis intersections, display coordinate values with text objects. Suitable for secondary school mathematics, ideal for teaching function graphs, introducing tangent concepts, and coordinate geometry applications.