Quadratic Equations

The trajectories of fireworks are modeled by quadratic equations. The equations can be used to predict the maximum height of a firework and the number of seconds it will take from launch to explosion. In this chapter, we will study the properties of quadratic equations, solve them, graph them, and see how they are applied as models of various situations.

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 and using it to solve quadratic equations with a leading coefficient of $1$ or another value.
• Solve Quadratic Equations Using the Quadratic Formula — using the Quadratic Formula to solve equations, using the discriminant to predict the number of solutions, and choosing an appropriate solution method.
• Solve Applications Modeled by Quadratic Equations — solving applications involving consecutive integers, geometry, rectangular areas, and projectile motion.
• Graphing Quadratic Equations in Two Variables — recognizing and graphing parabolas, finding their axes of symmetry, vertices, and intercepts, and solving maximum and minimum applications.

This chapter overview is adapted from Elementary Algebra 2e, Chapter 10 Introduction by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, © OpenStax, licensed under CC BY-NC-SA 4.0. Access the original for free at openstax.org. Changes: condensed the chapter introduction and recast the chapter outline as a section list.