Parabola with Parameters H, K, and Point A

This GeoGebra example dynamically illustrates how the vertex coordinates (h, k) and the parameter a affect the shape and position of a parabola, with point A serving as a draggable control to explore the standard form y = a(x - h)² + k. Core mathematical concepts include the standard form of quadratic functions, vertex coordinates, axis of symmetry, and translations/scalings of the parabola. Construction details: the Root and Extremum commands are used to compute the parabola's roots and extrema, while objects a, k, h act as parameter sliders, f and g are function graphs, text1 and text2 are dynamic labels, and points A, B, C mark key locations. This is suitable for middle and high school students learning quadratic function properties, parameter effects on graphs, and function transformations, as well as for teachers creating interactive lessons.