Introduction to Quadratic Equations - Mathematics (Senior Secondary)

This course provides a focused introduction to quadratic equations, a cornerstone of algebra. We will move beyond linear equations to explore expressions with a squared term, covering the essential skills needed for the first term curriculum. The course focuses on the factorisation method for solving quadratics and the process of forming equations from their roots. Quadratic equations are essential tools in a vast range of fields. They are used in physics to model projectile motion, in engineering to design parabolic structures like satellite dishes, and in finance to optimise profit. Mastering these introductory concepts is a non-negotiable step for anyone advancing in mathematics or the physical sciences. By the end of this course, you will be able to factorise any simple quadratic expression and use this method to find the roots of an equation. You will also learn to construct a quadratic equation if you are given its roots, providing a solid foundation before moving on to more advanced methods in later terms. This course is designed for students who have a solid foundation in linear equations and algebraic factorisation. It is a critical course for all students on the science track and serves as the gateway to the study of more complex polynomials and functions.

Enrolment valid for 12 months

Course Chapters

1. Introduction

This chapter introduces the concept of a quadratic equation. It defines its standard form and explains why it represents a significant step forward from linear equations. Key learning objectives include identifying a quadratic equation and understanding the new types of problems that can be solved.

Chapter lessons

1-1. Welcome

This lesson outlines the structure and goals of the course. It defines the quadratic equation and introduces the key skills to be learned, from solving to graphing.

2. Solving Quadratic Equations by Factorisation

This chapter focuses on the algebraic method of solving quadratic equations by factorisation. It builds on existing knowledge of integers to develop a systematic approach to finding roots. Key learning objectives include factorising quadratic expressions and mastering the use of the null factor law to solve quadratic equations.

Chapter lessons

2-1. Revision of factorization of integers

This lesson provides a quick but essential review of finding factors of integers. This skill is the foundation for successfully factorising algebraic expressions.

2-2. Factorization of quadratic expressions and equations

This lesson teaches the method for breaking down a quadratic expression into two linear factors. This is the core technical skill required for solving by factorisation.

2-3. Solution of quadratic equations by the null factor law

This lesson applies the principle that if the product of two factors is zero, then at least one of the factors must be zero. This allows for the roots of the equation to be found.

3. Forming and Graphing Equations

This chapter explores the relationship between the roots of a quadratic equation and its algebraic and graphical forms. It covers how to construct equations and visualise them as parabolas. Key learning objectives include forming a quadratic equation from its given roots and drawing a quadratic graph to obtain its roots visually.

Chapter lessons

3-1. Formation of quadratic equations with given roots

This lesson reverses the solving process, teaching the method for constructing a valid quadratic equation when its two solutions are already known.

3-2. Drawing quadratic graphs

This lesson introduces the graphical representation of a quadratic equation – the parabola. It covers how to plot key points to accurately sketch the curve.

3-3. Obtaining roots from a quadratic graph

This lesson connects the algebra to the geometry, explaining how to identify the roots (solutions) of a quadratic equation by finding where its graph intersects the x-axis.

4. Conclusion and Next Steps

This concluding chapter summarises the key concepts of quadratic equations, reinforcing the understanding of algebraic and graphical methods. It prepares the student for more advanced topics. Key outcomes include a review of the methods for solving, forming, and graphing quadratic equations, and an understanding of how this knowledge fits into the broader study of functions.

Chapter lessons

4-1. Summary of what you have learned

This lesson provides a concise overview of the entire course, recapping factorisation, forming equations from roots, and graphical interpretation.

4-2. A look ahead to polynomials and functions

This lesson places the acquired skills in context. It explains how quadratic equations are a specific type of polynomial function and how this knowledge is essential for more advanced algebra and calculus.