Investigating General Parabola (AASL 2.6)

This GeoGebra example dynamically explores the general parabola y = ax² + bx + c, illustrating how parameters a, b, and c affect the direction of opening, axis of symmetry, and vertex position, while linking to translation transformations and function graphs. Core mathematical concepts include quadratic functions, parabolas, conversion between standard and vertex forms, axis of symmetry, discriminant, and graph translations. Construction highlights: the Intersect command is used to find intersection points with coordinate axes; sliders or input boxes control parameters a, b, c; text objects display vertex, axis, and key point coordinates; auxiliary lines (e.g., axis of symmetry) and labeled points (vertex, intercepts) enhance visualization. Suitable for IB Mathematics Analysis and Approaches SL (AASL 2.6) or high school students studying quadratic functions and graph transformations, as well as for teacher demonstrations or student-led investigations of parameter effects.