# Ch 6: Quadratic Equations, Functions & Inequalities

### About This Chapter

## Quadratic Equations, Functions, and Inequalities - Chapter Summary

This chapter can help guide you through an engaging review delivered via video and text lessons. These lessons will comprehensively cover material on quadratic equations, functions, and inequalities. You will be reviewing how to use FOIL in reverse to factor quadratic equations, how to solve a quadratic equation by factoring, and how to solve quadratic equations not in standard form. Once you have completed all the lessons in this chapter you should confidently be able to:

- Define and give examples of a quadratic equation
- Solve a quadratic equation using the quadratic formula
- Explain the process for graphing a system of quadratic inequalities
- Give examples of quadratic functions
- Write quadratic functions
- Recognize differences between graphs of quadratic and linear functions

Using this convenient study chapter, you can quickly refresh your knowledge of this topic. You may use the lessons in any order, but be sure to take the quizzes at the end of each to quickly ascertain your skill level of a specific topic. At any time, you can use the timeline of the lesson to jump to a particular spot for another look. Lesson transcripts are also available should you choose to print them for a hard copy option.

### 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.

### 2. How to Write Quadratic Functions

In the real world, you won't always be given equations as you are in textbooks. Often, you'll need to find equations using a few points or other pieces of data. Learn how to find and write quadratic equations.

### 3. Quadratic Functions: Examples & Formula

Learn what sets quadratic functions apart from all other functions. Learn how you can spot a quadratic just by looking at its graph. Also learn the two formulas that will help you when working with them.

### 4. Comparing Graphs of Quadratic & Linear Functions

In this lesson, we will discuss the basics of linear and quadratic functions and their graphs. We will see some examples and discuss how to graph each type when given an equation.

### 5. 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.

### 6. 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.

### 7. 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!

### 8. Graphing & Solving Quadratic Inequalities: Examples & Process

When you finish watching this video lesson, you will be able to graph and solve your own quadratic inequality. Learn what steps you need to take and what to watch for.

### 9. Graphing a System of Quadratic Inequalities: Examples & Process

What is a system of quadratic inequalities? What are the steps to graphing them? Find the answers to these questions by watching this video lesson. When you finish, you will be able to graph these yourself.

### 10. 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.

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### Other Chapters

Other chapters within the NES Mathematics Middle Grades & Early Secondary (105): Practice & Study Guide course

- Overview of Mathematical Reasoning
- Introduction to Mathematical Problem Solving
- NES Math: Properties of Real Numbers
- Understanding Relations & Functions
- Overview of Linear Functions & Equations
- Overview of Polynomial Equations, Functions & Inequalities
- Working with Absolute Values
- Overview of Rational & Radical Functions
- NES Math: Piecewise Functions
- NES Math: Exponential & Logarithmic Functions
- Scientific Measurement Principles & Calculations
- NES Math: Foundations of Geometry
- NES Math: Geometric Figures
- Triangle Properties & Proofs
- NES Math: Parallel Lines & Polygons
- NES Math: Circles & Arc of a Circle
- NES Math: Conic Sections
- NES Math: Geometric Solids
- NES Math: Analytical Geometry
- Statistics: Principles & Techniques
- Probability: Principles & Techniques
- Overview of Discrete Mathematics
- Performing Operations on Matrices & Vectors
- Solving Problems with Sequences & Series
- NES Mathematics Middle Grades & Early Secondary Flashcards