Transformation of Quadratic Functions: Shifts, Stretches, and Intersections

①This example dynamically demonstrates how quadratic functions change under translations and stretches, using intersection points and slopes to reveal relationships between coefficients and geometric features. ②Core math concepts include standard and vertex forms of quadratics, graph transformations (shifts and stretches), function intersections, slope, optimization, and curve sketching, with integer parameters for exploration. ③Construction highlights: GeoGebra commands Intersect and Slope are used to create intercepts (Gyintercept, Fyintercept, etc.) and compute slopes of relevant lines; objects c, a, g, f, h, j, m and text labels text2, text3 enable interactive parameter adjustments. ④Suitable for high school students learning function transformations, coordinate geometry, and introductory calculus, as well as for classroom demonstrations or self-guided exploration of quadratic properties.