Completing the Square: Quadratic Graph Transformations

This example demonstrates how to complete the square for a quadratic function in general form, convert it to vertex form, and dynamically observe graph transformations including translation, opening direction, and extrema. Core concepts: completing the square for quadratic functions, vertex coordinates, and graph translation and scaling. Construction uses GeoGebra commands such as Extremum to find critical points, sliders to dynamically adjust parameters a, b, c, plot the function f(x)=ax²+bx+c in real-time, and text boxes to display the completing the square process and vertex coordinates, showing how parameter changes affect the graph. Suitable for middle school quadratic function graphing, high school function transformation review, and math competition practice.