Dynamic Exploration of Quadratic Function Graphs f(x)=ax²+bx+c

This GeoGebra example demonstrates the dynamic sketching of the quadratic function graph f(x)=ax²+bx+c as the real coefficients a, b, and c are adjusted. It visually illustrates how the parabola changes in opening direction, axis of symmetry, vertex position, and number of x-axis intersections. Core mathematical concepts covered include quadratic functions, parabolic properties, coefficient–graph relationships, roots/zeros, discriminant signs, monotonic intervals, and maximum/minimum values. The construction relies on GeoGebra commands such as Intersect, Line, and Textfield, together with objects including sliders a, b, c, the function f, text box boxf, intersection points X_1 and X_2, and multiple dynamic text fields for displaying expressions, signs, monotonicity, and extremum information. The resource is suitable for middle and high school mathematics instruction, classroom demonstrations, inquiry-based learning, and independent review of quadratic function graphs.