Parabola Flower (Sofia) — a Rotation-Based Geometry Construction

This example demonstrates how a “flower-like” pattern can be constructed by combining a parabola (and its rotated copies) using planar symmetry. It highlights key ideas such as parabolas as quadratic/power-function graphs and the geometric effect of rotation on curves in coordinate geometry. Construction-wise, it follows the provided GeoGebra commands: it uses Point and Rotate to define key elements (e.g., the curve/function f, an angle α, a center point A) and then produces rotated versions of the curve (f′, along with the corresponding point B). By rotating the original parabola around the chosen center by the specified angle(s), the individual petals are generated and assembled into the overall symmetric figure. Suitable for advanced high-school students and early university learners, especially for lessons on function graphs, geometric transformations, and model-building with GeoGebra.