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Ch 10: Solving & Graphing Quadratics

About This Chapter

This chapter will help you understand how to solve and graph quadratics. Take a look at the definition and examples of a quadratic equation, practice problems for completing a square, and more.

Solving & Graphing Quadratics - Chapter Summary

Let our experts present you with information on solving and graphing quadratics. You will discover problem-solving methods and learn about the proper use of the quadratic formula. Get details about factoring to solve a quadratic equation, the definition of a parabola, and standard, vertex, and intercept forms of a parabola. Additional topics include:

  • Definition, equation and proof of the quadratic formula
  • Quadratic formula examples
  • Finding a solution for quadratic inequalities using two binomials
  • Completion of a square
  • Quadratic trinomials and factoring
  • Solutions for quadratics not in standard form
  • Reflections: graphing across axes, the origin, and line Y=X
  • Quadratic equations, square roots and graphing

The fact that the lessons are broken up into short chunks makes it easy to make continuous progress on your study program. Whenever you have a few minutes, log in using your mobile device and go through some of the lessons. Track your progress on your dashboard.

15 Lessons in Chapter 10: Solving & Graphing Quadratics
Test your knowledge with a 30-question chapter practice test
What is the Quadratic Formula? - Definition, Equation & Proof

1. What is the Quadratic Formula? - Definition, Equation & Proof

The quadratic formula is a method that is used to find the roots of a quadratic equation. In this lesson, you will learn about the history of the quadratic formula, how to use it, and prove it. A quiz at the end will solidify what you've learned.

The Quadratic Formula: Definition & Example

2. The Quadratic Formula: Definition & Example

Watch this video lesson to learn how you can use the quadratic formula to solve certain types of problems. Learn what kinds of equations you can solve using this formula as well as how easy it is to use this formula.

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.

Solving Problems using the Quadratic Formula

4. 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.

What is a Quadratic Equation? - Definition & Examples

5. 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 Quadratic Inequalities Using Two Binomials

6. 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?

7. 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

8. 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.

How to Complete the Square

9. 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

10. 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!

How to Solve a Quadratic Equation by Factoring

11. 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!

Solving Quadratic Trinomials by Factoring

12. 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 Solve Quadratics That Are Not in Standard Form

13. 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 Graph Reflections Across Axes, the Origin, and Line y=x

14. How to Graph Reflections Across Axes, the Origin, and Line y=x

A graph can be reflected in three ways - across the axes, the origin and the line y = x. There are specific rules to perform each reflection. This lesson will describe those rules and show you how to perform these reflections.

Solving Quadratic Equations with Square Roots or Graphing the Function

15. Solving Quadratic Equations with Square Roots or Graphing the Function

Quadratic equations can be solved in many ways, including taking square roots and graphing the function. In this lesson, learn how to use these techniques to solve quadratic equations.

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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