Exploring Cubic Graphs and x-Intercepts

①This example dynamically demonstrates the link between the equation of a cubic function and its x-intercepts (roots), helping students visualize how algebraic expressions correspond to geometric graph features. ②Core mathematical concepts include cubic functions, polynomial roots, intersections with the x-axis, and the relationship between factorization and graph shape. ③Construction highlights: using GeoGebra's Intersect command to find points A, B, C where the function f meets the x-axis, and creating additional points D, E, F, G and text1 to label and display coordinates, allowing interactive exploration of different cubic equations. ④Suitable for high school students learning functions and equations, as well as introductory calculus courses, serving as a visual teaching aid to bridge symbolic algebra and graphical understanding.