Quadratic Applications in the Real World: Problem Analysis

This report investigates the application of quadratic equations in real-world scenarios, focusing on problem-solving techniques. It begins with an introduction to the challenges students face in understanding quadratic equations and then delves into specific problems, such as determining the cost and profit for a supermarket selling milk. The report derives formulas, constructs quadratic models, and presents graphical representations using Geogebra. It also explores profit maximization using differentiation. Furthermore, the report analyzes the trajectory of a free kick in soccer, formulating simultaneous equations and generating quadratic equations to model the ball's path. The study modifies parameters like the distance to the goal and the wall's height to assess the kick's success under varying conditions. This detailed analysis showcases the practical utility of quadratic equations in diverse contexts.