Parabola and Related Geometric Optimization Problems

This example demonstrates the basic graph of a parabola and its application in geometric optimization problems. Core mathematical concepts include the definition and equation of a parabola, roots (zeros), parallelograms, spheres, similar triangles, and optimization problems. Construction highlights: based on the construction summary, objects a and c are used, possibly with sliders or parameters to control the parabola's shape, and related geometric elements (such as parallelograms, spheres, similar triangles) are constructed to explore optimization relationships. Suitable for high school or early college students to understand the connection between parabola properties and geometric optimization, and can serve as dynamic exploration material.