Parabola through 3 Points

This example demonstrates how to construct a parabola passing through three given points and explores its geometric properties. The core mathematical concepts involve quadratic functions and conic sections, including the standard equation of a parabola, its axis of symmetry, and the uniqueness of a parabola determined by three non-collinear points. Construction highlights: using GeoGebra commands Extremum to find the vertex (extremum) of the parabola and OrthogonalLine to construct perpendicular lines or the axis of symmetry. Objects include points A, B, C, line d, coefficients a, b, c, function f, auxiliary point K, and line g. Suitable for middle and high school students learning quadratic function graphs and coordinate geometry, this interactive tool helps visualize how three points define a unique parabola and how changing parameters affects its shape.