Building Quadratic Functions to Describe Situations (Part 1): From Key Points to

This GeoGebra example demonstrates how to build quadratic function models step-by-step from a given situation, matching the resulting graphs to specified features. It focuses on key concepts such as the structure of quadratic functions (forms and parameter meaning), piecewise modeling to represent different behaviors on different intervals, and step-like conditions that trigger changes in the expression. The construction is organized around the provided objects A1, B1, A2, A3, A4, A5, and A6, which serve as the essential points/parameters used to determine the quadratic relationship and assemble the corresponding graph piece by piece. The activity is well-suited for late middle school through early high school (and introductory pre-calculus) students, especially for learning function modeling and graphing with piecewise definitions.