Parabola Parent Function Transformations: Effects of a, h, k

①This example uses dynamic sliders to visually demonstrate how the parameters a, h, and k in the quadratic parent function y = a(x-h)² + k affect the parabola's position, orientation, and vertical stretch, showing the combined influence on the graph's shape and location. ②Core mathematical concepts include the standard form of quadratic functions, vertex coordinates, axis of symmetry, direction of opening, and transformations such as horizontal/vertical translation and vertical scaling, fundamental to function transformation and coordinate geometry. ③Construction highlights: GeoGebra sliders (objects a, h, k) control each parameter; the Transformation object applies the mapping from the parent function to the new function; the Parent object marks the original parent parabola; text1 dynamically displays the current function expression, enabling real-time observation of how parameter changes correspond to graph changes. ④Suitable for middle-to-high school students learning properties of quadratic functions, as well as for teacher-led demonstrations or student self-exploration to grasp the effect of parameters on function graphs.