Cubic Function with Dynamic Parameters

① This GeoGebra example dynamically displays the graph of a cubic function f(x)=ax³+bx²+cx+d, allowing users to observe how changing coefficients affects the curve's shape, inflection points, and monotonicity. ② Core mathematical concepts include cubic polynomial functions, derivatives and extrema, transformations of function graphs (translation and scaling), and the geometric meaning of parameters a, b, c, and d. ③ Construction highlights: sliders are used to define parameters a, b, c, and d, and the function f is entered as f(x)=a*x^3+b*x^2+c*x+d; dragging the sliders updates the graph in real time. The objects listed in the construction summary (a, b, c, d, f) correspond to these parameters and the function. ④ Suitable for high school and early college students learning polynomial functions, and for teachers as a classroom demonstration tool to build intuitive understanding of parameter-image relationships.