Henan 2019 Middle School Exam Q23: Quadratic Function with Geometric Transformat

This GeoGebra example dynamically illustrates Problem 23 from the 2019 Henan Middle School Entrance Exam, which integrates a quadratic function with geometric figures such as trapezoids and rhombuses. It explores relationships among segments, angles, and symmetry through rotation and reflection. Core mathematical concepts include the graph of quadratic functions, the Pythagorean theorem, properties and criteria for rhombuses and trapezoids, geometric transformations (rotation and mirroring), perpendicular lines, midpoints, and angle measurement. The construction utilizes key GeoGebra commands including Intersect, Point, OrthogonalLine, Polygon, Angle, Mirror, Segment, Midpoint, and Line to define objects like functions f and g, points A–I, J, K, and auxiliary lines h, i, j, etc., enabling interactive verification of geometric conjectures. This resource is ideal for Grade 9 students preparing for high-stakes exams, particularly for mastering the synthesis of algebraic functions and synthetic geometry.