# Ch 3: Quadratic Functions

### About This Chapter

## Quadratic Functions - Chapter Summary and Learning Objectives

The lessons in this course cover the functions necessary to master quadratic equations. You'll learn various methods of solving quadratic equations. Other lessons cover the graphing of quadratic inequalities and graphing systems of quadratic inequalities. This chapter is designed to teach you:

- The definition of a parabola and about parabolas in various forms
- To factor quadratic equations
- To solve quadratic equations using the quadratic formula or through factoring
- To graph quadratic inequalities

Video | Objective |
---|---|

What is a Parabola | Defining and recognizing a parabola. |

Parabolas in Standard, Intercept and Vertex Form | Exploring various methods of expressing the equation of a parabola. |

How to Factor Quadratic Equations: FOIL in Reverse | Reversing the FOIL method to factor quadratic equations. |

Factoring Quadratic Equations: Polynomial Problems with a Non-1 Leading Coefficient | Factoring quadratic trinomials in which the leading coefficient is not 1. |

How to Complete the Square | Solving equations by completing the square. |

Completing the Square Practice Problems | Practice in completing the square. |

How to Solve a Quadratic Equation by Factoring | Solving a quadratic equation by factoring. |

How to Use the Quadratic Formula to Solve a Quadratic Equation | Solving a quadratic equation with the quadratic formula. |

How to Solve Quadratics with Complex Numbers as the Solution | Solving quadratics with complex numbers as the solution. |

Graphing and Solving Quadratics | Graphing quadratic inequalities and identifying the regions that satisfy the inequalities. |

Graphing a System of Quadratic Inequalities | Graphing systems of quadratic inequalities and identifying the regions that satisfy the inequalities. |

### 1. 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.

### 2. 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.

### 3. Identifying Conic Sections: General Form & Standard Form

Did you know that if you slice a cone in different ways, you can make a circle, an ellipse, a parabola or a hyperbola? And, did you know that you can express all these shapes with just one general equation?

### 4. 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.

### 5. 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!

### 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.

### 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!

### 8. 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!

### 9. 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.

### 10. 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.

### 11. 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.

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### Other Chapters

Other chapters within the Math 105: Precalculus Algebra course

- Mathematical Modeling
- Linear Equations & Inequalities
- Rational Expressions and Functions
- Polynomial Functions of a Higher Degree
- Absolute Value Equations & Inequalities
- Complex Numbers
- Geometry Basics
- Functions Overview
- Function Operations
- Graph Symmetry
- Exponential and Logarithmic Functions
- Introduction to the Derivative
- Studying for Math 105