Building Quadratic Functions from Situations (Part 3)

This example demonstrates how to model a real geometric situation with a quadratic function, then verify the model by using a constructed geometric configuration. The key ideas are quadratic function construction (determining coefficients from conditions), ratio-based relationships arising from geometry, and circle-related constraints (e.g., circumcircle/circumscribed-circle type structures). It also leverages triangle and special quadrilateral patterns such as kite-like configurations to create the necessary algebraic conditions. From the construction summary, multiple point objects—A1, B1, D1, A2 through A9, and C1—are used to build the geometric skeleton; those interdependent point placements encode the ratio/length constraints. The resulting relationships are then translated into the quadratic function parameters, producing a function graph consistent with the modeled situation. Suitable for secondary-school students learning function modeling and geometry, as well as for GeoGebra users who want a geometry-to-function construction workflow.