Completing the Square (Part 2): Geometric Construction of a Perfect Square

This example demonstrates how to complete the square for a quadratic expression by using a step-by-step geometric construction, making the algebraic transformation visible. It focuses on the key ideas behind completing the square, the vertex (completed-square) form of a quadratic function, and the correspondence between arithmetic/powers in algebra and the matching structure in a constructed figure. Construction-wise, it uses Polygon and Segment to build the geometric pieces and partitions, while Sequence generates ordered points or “steps” to guide the transformation process. Textfield and related text objects are used to input parameters and display coefficients/constants during the demonstration. Multiple function objects (e.g., f, g, h, i) help visualize relationships across stages, and interactive buttons (button1–button7) together with an input box (inputBox1) support an incremental, student-friendly walkthrough. Suitable for middle and high school math learning, especially for teaching quadratic functions and using geometric intuition to justify algebraic identities.