Quadratic Function: Determine the Equation Passing Through Any Three Points

This GeoGebra example demonstrates how to uniquely determine a quadratic function (parabola) that passes through any three non-collinear points in the plane. It involves core mathematical concepts such as the general form of a quadratic function y = ax² + bx + c, solving a system of three linear equations, and the correspondence between algebraic expressions and their graphs. The construction uses interactive input fields for point coordinates (e.g., A_x, A_y, B_x, etc.) and multiple text objects (text1 through text13) to dynamically display the computed coefficients and resulting equation. Suitable for upper middle school or high school mathematics instruction, this tool supports teaching function fitting, applications of linear systems, and foundational coordinate geometry, and encourages student exploration of the conditions under which three points define a parabola.