Translating a Parabola Up or Down

①This GeoGebra example demonstrates the vertical translation of a parabola (upward or downward) through an interactive animation, showing how the graph shifts along the y-axis. ②Core mathematical concepts include quadratic function transformations, specifically vertical shifts (e.g., y=x² to y=x²+k), along with related ideas such as parametric curves, continuity, and the Pythagorean theorem. ③Construction highlights: the use of Button objects to trigger the translation, a function f representing the parabola, and text1 to display the current shift value; sliders or buttons control the translation distance for dynamic visualization. ④This resource is suitable for middle and high school students learning quadratic function properties, graph transformations, or geometric intuition, and can be used in classroom demonstrations or self-directed exploration of translation rules.