The Basic Parabola Equation y=ax²: Dynamic Exploration

This GeoGebra example demonstrates the basic parabola y = ax² and how its shape and position on the plane change when the coefficient a is varied. The core mathematical concept is the relationship between the quadratic function's graph and its leading coefficient, including the direction of opening (upward for a>0, downward for a<0) and the width of the parabola (narrower for larger |a|). Construction details: a slider controls the parameter a; the Point command creates points on the parabola; OrthogonalLine and Intersect are used to construct perpendicular lines and their intersection points; Segment connects relevant points; text objects (text1 to text4) display coordinates for visual feedback. This resource is suitable for middle school to high school students learning quadratic function graphs, and for teachers demonstrating parameter effects in class.