Dynamic Parabola XII: Curve Sketching 01

This example demonstrates how to explore the shape of a parabola through dynamic parameters, using auxiliary lines, intersection points, and other geometric constructions. The core mathematical concepts include quadratic functions, translation and dilation of parabolas, and curve sketching techniques. Construction highlights: GeoGebra commands such as Intersect, Point, OrthogonalLine, Segment, and Distance are used; objects include parameters a, α, β, equations eq1 to eq4, and numerous points, lines, and functions like A_1, S_1, f, Z_1, P_1, h, M_1, i, g, EA, S_2, Z_2, p, q, r, L_1', L_2', P_2, j, k, l, A_3, m, N_2, A_2, n, L_2, L_1, s, N_1, O, etc., showcasing rich dynamic geometry interaction. Suitable for high school or early college students studying analytic geometry and introductory calculus, this example helps understand parabola properties and dynamic graphing methods.