# Ch 5: Working with Quadratic Functions

Watch online math video lessons to learn about parabolas, quadratic inequalities, perfect squares and more. Use the quizzes that follow each lesson to test your knowledge of quadratic functions.

## Working with Quadratic Functions - Chapter Summary and Learning Objectives

Now that you've been introduced to quadratics in the previous chapter, use this one to further explore the relationship between these types of equations and their graphs. You can also try out advanced methods for factoring and solving quadratic equations - regardless of whether they have a leading coefficient of one or higher - along with techniques for graphing systems of quadratic inequalities used to model data sets or chart projectile motion. Watch the video lessons in this chapter and learn how to:

• Write the equation of a parabola in its various forms
• Factor quadratics and convert a polynomial into a perfect square
• Solve quadratic equations with real and complex numbers

Video Objectives
What Is a Parabola? Get some examples of parabolas in everyday life and learn how to identify their maximum height, vertex, axis of symmetry and intercepts.
Parabolas in Standard, Intercept, and Vertex Form View examples of quadratic equations written in standard, intercept and vertex forms. Check out their graphs.
How to Factor Quadratic Equations: FOIL in Reverse Review the processes involved in multiplying binomials. Learn how to factor equations by performing this process in reverse.
How to Complete the Square Find out what it takes to turn a polynomial into a perfect square binomial.
Completing the Square Practice Problems Get extra practice converting the standard form of a quadratic equation into the vertex form. Convert a trinomial into a binomial by completing the square.
How to Solve a Quadratic Equation by Factoring Learn how factoring and the zero product property can be used to solve quadratic equations.
How to Solve Quadratics with Complex Numbers as the Solution Discover the uses of the discriminate to determine whether the solution to an equation contains real or complex numbers. Practice solving quadratics that include complex numbers.
Graphing & Solving Quadratic Inequalities: Examples, Lesson & Quiz Get the definition of a quadratic inequality. Learn how to solve and graph these types of equations.
Graphing a System of Quadratic Inequalities: Examples, Lesson & Quiz Discover methods for graphing quadratic inequalities as well as systems of quadratic inequalities.
Applying Quadratic Functions to Motion Under Gravity and Simple Optimization Problems Understand how quadratic functions can be used to model projectile motion and solve optimization problems.
Using Quadratic Functions to Model a Given Data Set or Situation Explore the uses of quadratic functions to model data sets.

12 Lessons in Chapter 5: Working with Quadratic Functions
Test your knowledge with a 30-question chapter practice test
Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

### Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.