Students engage with various methods to solve quadratic equations, including factoring, completing the square, and using the quadratic formula. Through diverse exercises, they learn to determine the roots of quadratic equations and understand the conditions under which different methods are most effective. Mastering these techniques prepares students for more complex algebraic challenges and enhances their problem-solving skills.

Quadratic equations, characterised by the highest exponent being two, form a fundamental part of algebra. Students will explore the structure and components of these equations, such as the coefficients and the constant term, and how they affect the graph and solutions of the equation. They will also investigate how the discriminant determines the nature and number of solutions. This deep dive into quadratics lays the groundwork for further mathematical exploration and applications.

Students discover the practical applications of quadratic equations in various settings, such as physics, engineering, economics, and even sports. For example, they learn how quadratics are used to model trajectories in ball sports, optimise profit in business scenarios, and calculate braking distances in automotive safety. These real-world examples demonstrate the utility of quadratic equations in solving practical problems and making predictions, thereby illustrating the value of algebra in everyday life and professional practices.