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Ch 15: Solving Quadratic Equations

About This Chapter

This chapter is designed to boost your knowledge of the process of solving quadratic equations. Take a look at the definition and examples of a quadratic equation, practice problems for completion of the square, and more.

Solving Quadratic Equations - Chapter Summary

This chapter was developed by our experts to increase your understanding of the steps involved in solving quadratic equations. Review information on solving a quadratic equation using the quadratic formula, arriving at quadratic trinomial solutions by factoring, the definition of a parabola, and finding solutions for inequalities using two binomials. Additional lesson material includes:

  • Multiplication property of zero and assigning the greatest common factor
  • Solving quadratics by factoring
  • Solving quadratics not in standard form
  • Completion of the square
  • Calculating solutions for equations with literal coefficients by using the quadratic formula
  • FOIL in reverse for factoring quadratic equations
  • Polynomial problems with a non-1 leading coefficient
  • Standard, vertex, and intercept forms of parabolas

Short videos comprise the chapter. The lessons are about 5-10 minutes long. Log in using your mobile device whenever you have a few minutes and complete some lessons. You can track your progress on your dashboard.

15 Lessons in Chapter 15: Solving Quadratic Equations
Test your knowledge with a 30-question chapter practice test
What is a Quadratic Equation? - Definition & Examples

1. What is a Quadratic Equation? - Definition & Examples

You might be surprised to learn that quadratic equations are an important part of the world we live in. We sometimes even make use of them for our entertainment! Watch this video lesson to learn more about these equations.

Solving Quadratics: Assigning the Greatest Common Factor and Multiplication Property of Zero

2. Solving Quadratics: Assigning the Greatest Common Factor and Multiplication Property of Zero

When it comes to solving quadratics, we have at our disposal several methods. Watch this video lesson to learn one such method you can use to solve quadratics that don't have a constant term.

How to Use the Quadratic Formula to Solve a Quadratic Equation

3. How to Use the Quadratic Formula to Solve a Quadratic Equation

When solving a quadratic equation by factoring doesn't work, the quadratic formula is here to save the day. Learn what it is and how to use it in this lesson.

How to Solve a Quadratic Equation by Factoring

4. How to Solve a Quadratic Equation by Factoring

If your favorite video game, 'Furious Fowls,' gave you the quadratic equation for each shot you made, would you be able to solve the equation to make sure every one hit its target? If not, you will after watching this video!

How to Solve Quadratics That Are Not in Standard Form

5. How to Solve Quadratics That Are Not in Standard Form

It isn't always the case that your equation will be set up nicely for you to solve. In this lesson, learn how to factor or use the quadratic formula to solve quadratic equations, even when they are not in standard form.

How to Complete the Square

6. How to Complete the Square

Completing the square can help you learn where the maximum or minimum of a parabola is. If you're running a business and trying to make some money, it might be a good idea to know how to do this! Find out what I'm talking about here.

Completing the Square Practice Problems

7. Completing the Square Practice Problems

Completing the square is one of the most confusing things you'll be asked to do in an algebra class. Once you get the general idea, it's best to get in there and actually do a few practice problems to make sure you understand the process. Do that here!

Using the Quadratic Formula to Solve Equations with Literal Coefficients

8. Using the Quadratic Formula to Solve Equations with Literal Coefficients

Watch this video lesson to find out what steps you need to take to solve equations with literal coefficients using the quadratic formula. Learn why it might be easier to work with literal coefficients than with number coefficients.

Solving Problems using the Quadratic Formula

9. Solving Problems using the Quadratic Formula

The quadratic formula is not as complicated as it may look. You can learn to tackle this formula and succeed in using it to help you solve your quadratic problems. Watch this video to see how.

Solving Quadratic Trinomials by Factoring

10. Solving Quadratic Trinomials by Factoring

Factoring is a quick and easy way to find the solutions to a quadratic trinomial. Watch this video lesson to learn how you can use this method to solve your quadratics.

How to Factor Quadratic Equations: FOIL in Reverse

11. How to Factor Quadratic Equations: FOIL in Reverse

So, you know how to multiply binomials with the FOIL method, but can you do it backwards? That's exactly what factoring is, and it can be pretty tricky. Check out this lesson to learn a method that will allow you to factor quadratic trinomials with a leading coefficient of 1.

Factoring Quadratic Equations: Polynomial Problems with a Non-1 Leading Coefficient

12. Factoring Quadratic Equations: Polynomial Problems with a Non-1 Leading Coefficient

Once you get good at factoring quadratics with 1x squared in the front of the expression, it's time to try ones with numbers other than 1. It will be the same general idea, but there are a few extra steps to learn. Do that here!

Solving Quadratic Inequalities Using Two Binomials

13. Solving Quadratic Inequalities Using Two Binomials

Watch this video lesson to learn what simple steps you can take to solve quadratic inequalities using two binomials. See how it only requires a few steps to solve quadratic inequalities using this method.

What is a Parabola?

14. What is a Parabola?

A parabola is the U shape that we get when we graph a quadratic equation. We actually see parabolas all over the place in real life. In this lesson, learn where, and the correct vocab to use when talking about them.

Parabolas in Standard, Intercept, and Vertex Form

15. Parabolas in Standard, Intercept, and Vertex Form

By rearranging a quadratic equation, you can end up with an infinite number of ways to express the same thing. Learn about the three main forms of a quadratic and the pros and cons of each.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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