Construct a Piecewise Quadratic Function via Reflection and Angle Bisectors

This example demonstrates how to build a piecewise quadratic function using geometric constructions involving circles and reflection symmetry, and then determine the relevant intersection points between the constructed pieces. Key concepts include piecewise functions modeled through geometry, properties of quadratic functions, circle–line (or segment) intersection relationships, and the role of angle bisectors and mirror transformations in enforcing geometric constraints. Construction highlights: Circle is used to create the key circle geometry (objects such as c, C); Mirror constructs reflected points to realize symmetry constraints (e.g., a and a′); LineBisector generates an angle bisector to define consistent angular relations; and Point, Segment, Polygon, and Angle are used to assemble the required vertices/edges (including trapezoid-like polygon structure). Intersection of the resulting geometric entities supports the piecewise behavior and the final key intersection locations. Suitable for high-school geometry–function integration, modeling lessons, and enrichment activities focusing on transformations and graphing.