Modeling Situations with Quadratic Functions (Part 1): Construction & Insight

This example demonstrates how to build a quadratic function step-by-step from a situation, then use the resulting graph to interpret the underlying relationship. It emphasizes key ideas in quadratic modeling, including the characteristic shape of a parabola, selecting parameters using ratios and rational numbers, and understanding how related expressions can be treated as piecewise when different conditions apply. Construction-wise, the provided object list (A3, B3, A4–A9, B4–B6, A1, D1, D3, E3, D4–D8, E4–E6, D9) indicates a workflow driven by multiple key points (A* and B* as geometric/coordinate anchors) together with auxiliary points or measures (D* and E*) to determine coefficients and place the graph correctly for verification. Suitable for middle to high school students learning functions and graphing, and for classroom GeoGebra explorations focused on algebra-to-visual modeling.