Throughout this specialization, we will use functions to help visualize, analyze, and interpret the relationships between variables. In this module, we will start by exploring linear functions. A linear relationship between two variables occurs when changes in one variable correspond to proportional changes in the other. Many physical situations can be modeled using linear functions. We will see examples of how to create and interpret linear functions in the sections that follow.

We will now add to our library of functions by exploring quadratic functions. Adding an extra term with x-squared to a linear function creates a quadratic function. The graphs of these functions are parabolas, which can be used to model things like the path of a projectile or the curved surface of a satellite dish. In this module, we will examine the key parts of the graphs of quadratic functions, and explore strategies to fit quadratic functions to real-world data.

We will wrap up our first course by combining our previous knowledge of systems of equations and inequalities with quadratic functions. Adding squared terms to systems of equations and inequalities, we can describe more elaborate regions in the plane. This allows us to model a wider range of scenarios.