Constructing Quadratic Functions from Geometric Patterns

This GeoGebra example demonstrates how to build a quadratic function starting from a geometric repeating pattern and the measurements implied by the construction. It highlights key ideas such as polynomial functions (especially quadratic functions), arithmetic/sequence-like construction logic, and a sum/area viewpoint that can connect to upper/lower sums or Riemann-sum thinking when interpreting accumulated geometric quantities. In the construction, several key objects—A1, B1, C1, D1, A2, A3, A4, A5—serve as anchor points or geometric markers that capture the pattern’s structure and sampling positions. Those objects are then used to establish the geometric-to-algebra correspondence and to generate the resulting second-degree relationship and graph. Suitable for middle to high school math (function modeling and graphing), as well as classroom demonstrations and exploratory learning with parameter changes.