# Ch 16: Factoring & Graphing Quadratic Equations

### About This Chapter

## Factoring & Graphing Quadratic Equations - Chapter Summary and Learning Objectives

Since visual representations of data can be very beneficial for real-life purposes, this chapter offers essential information about various types of tables and graphs, including scatterplots and line graphs. Expert instructors will also guide your study of multiplying binomials, factoring quadratic equations and completing the square. By the time you've wrapped up this set of lessons, you should have a solid understanding of the following topics and procedures:

- Using FOIL and the area method for multiplying binomials
- FOIL in reverse for factoring
- Solving quadratic trinomials with factoring
- Methods for completing the square

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

Using Tables and Graphs in the Real World | Find out how graphs and tables can be used to represent real-life information. |

Scatterplots and Line Graphs: Definitions and Uses | Take a closer look at how scatterplots and line graphs can be used to represent real info. |

Multiplying Binomials Using FOIL and the Area Method | Become acquainted with FOIL (First, Outer, Inner, Last) and the area method for multiplication of binomials. |

Multiplying Binomials Using FOIL and the Area Method: Practice Problems | These problems can help you practice applying your knowledge of how to use FOIL and the area method to multiply binomials. |

How to Factor Quadratic Equations: FOIL in Reverse | Explore FOIL in reverse when factoring quadratic equations. |

Factoring Quadratic Equations: Polynomial Problems with a Non-1 Leading Coefficient | Learn how to factor polynomials with non-1 leading coefficients. |

Solving Quadratic Trinomials by Factoring | Examine the steps for using factoring when solving quadratic trinomials. |

How to Complete the Square | Watch the experienced instructor show you strategies for completing the square. |

Completing the Square Practice Problems | Successfully complete practice exercises to become adept at completing the square. |

How to Solve a Quadratic Equation by Factoring | Explore methods for using factoring to solve quadratic equations. |

### 1. Using Tables and Graphs in the Real World

We use tables and graphs in algebra as ways to visually show an equation or function. But do we really use these in the real world? Is it that important to learn about tables and graphs? Find out in this video lesson.

### 2. Scatterplots and Line Graphs: Definitions and Uses

After watching this video, you will be able to understand scatter plots and line graphs. You will also be able to use them to tell people a story about what you see and observe. You will also be able to read them.

### 3. Multiplying Binomials Using FOIL and the Area Method

From the distributive property, to FOIL, to the area model, to happy faces and claws, there are many different ways to learn how to multiply binomials. In this lesson, you'll learn how to use all of them and get to pick which one you like the most.

### 4. Multiplying Binomials Using FOIL & the Area Method: Practice Problems

There are a few mistakes that are easy to make when multiplying binomials with FOIL and also a few ways to complicate problems like this, so why not make sure you're brushed up on your skills? You'll also learn a shortcut and how to use the area method to multiply even bigger polynomials.

### 5. 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.

### 6. 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!

### 7. 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.

### 8. 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.

### 9. 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!

### 10. 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!

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### Other Chapters

Other chapters within the Algebra 2 and Trig Textbook course

- Identifying Real Numbers
- Complex Numbers
- Absolute Value Review
- Solving Algebraic Expressions & Equations
- Calculating Rational Expressions
- Working with Linear Equations
- Solving & Graphing Inequalities
- Graphing & Working with Trigonometric Functions
- Graph Symmetry
- Graphing with Functions Review
- Solving Linear Equations
- Calculating & Graphing Polynomials
- Calculating & Simplifying Exponential Expressions
- Square Roots & Radical Expressions
- Quadratic Equations & Formulas
- Conic Sections: Ellipses, Circles, Hyperbolas & Parabolas
- Vectors, Matrices and Determinants
- Exponential Functions & Logarithmic Functions
- Arithmetic & Geometric Sequences & Series
- Calculating & Presenting Statistics
- Combinatorics & Probability
- Using Trigonometric Functions
- Trigonometric Graphs
- Trigonometric Applications
- Solving Trigonometric Equations
- Trigonometric Identities
- Circles, Angles & Circular Arcs