Parabolas between Parabolas: Nested Parabola Construction

① This example demonstrates the geometric phenomenon of generating a family of nested parabolas between two boundary parabolas, showing how a sequence of quadratic curves fills the region between them. ② Core mathematical concepts include quadratic functions, polynomials, plane curves, and transformations of function graphs, involving properties of real numbers. ③ Construction highlights: using GeoGebra's Polynomial command to define multiple polynomial functions, with points A, B, C as control points, generating parabolas f, g, h, and text objects text1, text2, text3 for labeling; sliders or parameters allow dynamic adjustment. ④ Suitable for high school or early college students to understand quadratic graphs, polynomial interpolation, and families of functions, as well as to explore positional relationships and geometric constructions between parabolas.