About This Chapter
Algebra II: Graphing and Factoring Quadratic Equations Review - Chapter Summary and Learning Objectives
The chapter starts with a look at how to use tables, scatterplots and graphs in real-life situations. You'll also learn to solve quadratic equations using the FOIL method. Later lessons show you how to solve quadratic trinomials and quadratic equations through factoring. By the end of the chapter, you should hold a good grasp of the following mathematical topics:
- Scatterplots and line graphs
- Parabolas in standard, intercept and vertex form
- FOIL method for multiplying binomials
- Quadratic equations
- Quadratic trinomials
- Completing the square
|Using Tables and Graphs in the Real World||Understand how to use graphs and tables in the real world to relay information.|
|Scatterplots and Line Graphs: Definitions and Uses||Define and read the information contained in scatterplots and line graphs.|
|What Is a Parabola?||Learn about a parabola's vertex, maximum, intercepts, roots and axis of symmetry.|
|Parabolas in Standard, Intercept and Vertex Form||Identify the three forms of parabolas: the standard, intercept and vertex.|
|Multiplying Binomials Using FOIL and the Area Method||Employ the FOIL method to multiply binomials.|
|Multiplying Binomials Using FOIL and the Area Method: Practice Problems||Solve practice problems multiplying binomials using the FOIL method.|
|How to Factor Quadratic Equations: FOIL in Reverse||Use the FOIL method in reverse to factor a quadratic equation.|
|Factoring Quadratic Equations: Polynomial Problems with a Non-1 Leading Coefficient||Determine how to factor a non-1 leading coefficient by grouping.|
|Solving Quadratic Trinomials by Factoring||Successfully answer quadratic equation problems with three terms.|
|How to Complete the Square||Understand how to properly complete the square.|
|Completing the Square Practice Problems||Solve practice sets that ask you to complete the square.|
|How to Solve a Quadratic Equation by Factoring||Determine how to solve a quadratic equation by factoring and using the zero product property.|
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. 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.
4. 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.
5. 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.
6. 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.
7. 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.
8. 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!
9. 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.
10. 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.
11. 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!
12. 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 within the Algebra II: High School course
- Algebra II: Real Numbers
- Algebra II: Complex and Imaginary Numbers Review
- Algebra II: Exponents and Exponential Expressions Review
- Algebra II: Properties of Functions Review
- Algebra II: Linear Equations Review
- Algebra II: Systems of Linear Equations
- Algebra II: Inequalities Review
- Algebra II: Absolute Value Review
- Algebra II: Quadratic Equations
- Algebra II: Factoring
- Algebra II: Polynomials
- Algebra II: Rational Expressions
- Algebra II: Graphing and Functions
- Algebra II: Conic Sections
- Algebra II: Roots and Radical Expressions Review
- Algebra II: Exponential and Logarithmic Functions
- Algebra II: Sequences & Series
- Algebra II: Combinatorics
- Algebra II: Calculations, Ratios, Percent & Proportions Review
- Algebra II: Statistics
- Algebra II: Trigonometry
- Homeschool Resources for High School Algebra II