Effects of Parameter a on the Graph of f(x)=ax²: Focus and Directrix

This applet dynamically demonstrates how the parameter a in the quadratic function f(x)=ax² affects the parabola's opening direction, width, and the positions of its focus and directrix. Core mathematical concepts include quadratic function graphs, the geometric definition of a parabola (locus of points equidistant from focus and directrix), the relationship between parameter a and focal length, and how focus and directrix shift as a changes. Construction highlights: using a slider for parameter a, and GeoGebra commands such as Point, Intersect, Circle, Line, Segment, and OrthogonalLine to construct the parabola, focus F, directrix g, and auxiliary geometric elements, providing dynamic visual feedback. Suitable for high school students learning quadratic functions and conic sections, as well as for classroom demonstrations or self-guided exploration of how parameters affect function graphs.