What is the connection between slices of a cone and the trajectory of a football? Between the geometry of the great pyramid and the tax bracket that you might be in? Between studying the protein content of bugs and comparing internet speeds? In this course we explore a range of interesting and practical real-world relationships hinging on the interplay between the linear and the quadratic. Study real-world connections using algebra and geometry In this free online course, we’ll look at a wide spectrum of interesting, and often surprising, mathematical relationships in our everyday world. These real-world interconnections can be studied using algebra and visualised concretely using graph paper and pencil, along with modern technologies such as graphing calculators and interactive graphing software. Linear and quadratic functions and their graphs allow us to make predictions, evaluate actions and test theories about many things - such as the maximal grade of railways, the trajectory of a football, the relationship between supply and demand in economics, and the difference between momentum and kinetic energy in physics. Linear and quadratic relations are balanced between algebra and geometry, with numerous connections to real life. Explore linear and quadratic relationships Our journey begins with the fundamental idea of direct proportionality. In the first week you’ll meet lots of examples of linear relationships in the world around us. Then you’ll learn to represent these relationships algebraically and graph them geometrically in the Cartesian plane to aid in visualisation. In subsequent weeks, we’ll look at quadratic relations from Apollonius to Bezier. We’ll discuss the history, look at lots of practical examples, and show you how to solve an interesting variety of concrete problems. Gain valuable skills for further study Understanding basic mathematical relationships is vital to many fields of study: biology, engineering, business, economics, political science and design. By the end of this course, you’ll have hands-on experience with a wide range of explicit examples, be familiar with a core area of pre-calculus mathematics, and be ready to go on to more advanced study of more sophisticated algebraic topics such as inverse relations and power laws. Whether you’re encountering these topics for the first time or brushing up on your high school mathematics, we hope you’ll actively join our community on this journey through some fascinating and practical topics that have contributed much to our understanding of the world around us.