Quadratic Equations and Functions

Blink your eyes. You’ve taken a photo. That’s what will happen if you are wearing a contact lens with a built-in camera. Some of the same technology used to help doctors see inside the eye may someday be used to make cameras and other devices. These technologies are being developed by biomedical engineers using many mathematical principles, including an understanding of quadratic equations and functions. In this chapter, you will explore these kinds of equations and learn to solve them in different ways. Then you will solve applications modeled by quadratics, graph them, and extend your understanding to quadratic inequalities.

Sections

• Solve Quadratic Equations Using the Square Root Property — solving quadratic equations of the forms $ax^2=k$ and $a(x-h)^2=k$ using the Square Root Property.
• Solve Quadratic Equations by Completing the Square — completing the square of a binomial expression and solving quadratic equations by completing the square.
• Solve Quadratic Equations Using the Quadratic Formula — using the Quadratic Formula, using the discriminant to predict the number and type of solutions, and choosing an appropriate solution method.
• Solve Equations in Quadratic Form — identifying a substitution, solving the resulting quadratic equation, and substituting back.
• Solve Applications of Quadratic Equations — solving number, geometry, projectile-motion, uniform-motion, and work applications modeled by quadratic equations.
• Graph Quadratic Functions Using Properties — finding a parabola’s axis of symmetry, vertex, and intercepts, graphing with these properties, and solving maximum and minimum applications.
• Graph Quadratic Functions Using Transformations — graphing with vertical and horizontal shifts, stretches, compressions, and reflections, and finding a quadratic function from its graph.
• Solve Quadratic Inequalities — solving quadratic inequalities graphically and algebraically and writing solutions in interval notation.

This chapter overview is adapted from Intermediate Algebra 2e, Chapter 9 Introduction by Lynn Marecek and Andrea Honeycutt Mathis, © OpenStax, licensed under CC BY-NC-SA 4.0. Access the original for free at openstax.org. Changes: omitted the opening photograph and its caption and recast the chapter outline as a section list.