Graph of y = ax²: Dynamic Exploration of Quadratic Functions

This GeoGebra example dynamically visualizes the graph of the quadratic function y = ax², allowing users to adjust the parameter a via a slider and observe how the parabola's opening direction, width, and vertex position change in real time. The core mathematical concepts include the standard form of quadratic functions, axis of symmetry, vertex coordinates, and the effect of the leading coefficient on the curve's shape. The construction uses GeoGebra commands such as If for conditional logic and TableText to generate a data table, along with multiple point objects (A1–A12, B1–B12) plotted on the curve to illustrate corresponding values. A slider controls the coefficient a of the function f, enabling interactive exploration. This resource is suitable for middle school to high school students learning quadratic function properties, as well as for teachers demonstrating the relationship between parameter changes and graph transformations, fostering visual and dynamic mathematical thinking.