About This Chapter
Quadratic Equations and Functions - Chapter Summary and Learning Objectives
This chapter introduces algebraic concepts including the quadratic formula, factoring, and completing the square. You will receive refresher information on principles you need to know to assimilate new steps, and you'll be guided through different processes and methods used to solve functions and quadratic equations. The lessons in this chapter are designed to help you:
- Become familiar with the quadratic formula
- Factor quadratic equations
- Solve non-standard-form quadratics
- Know how to complete the square
|How to Solve Quadratics That Are Not in Standard Form||Learn how to algebraically re-form non-standard quadratics into standard form.|
|How to Use the Quadratic Formula to Solve a Quadratic Equation||Understand when and how to solve quadratic equations with the quadratic formula.|
|How to Solve a Quadratic Equation by Factoring||Know how to use factoring to find the solution to a quadratic equation.|
|Factoring Quadratic Equations: Polynomial Problems with a Non-1 Leading Coefficient||Learn the steps involved in factoring quadratics that don't have 1 as the leading coefficient.|
|How to Factor Quadratic Equations: FOIL in Reverse||Use the FOIL (first, outer, inner, and last terms) method in reverse to factor quadratic equations.|
|Completing the Square Practice Problems||Undergo sample problems to ensure comprehension of how to complete the square.|
|How to Complete the Square||Understand how to convert a standard-form quadratic equation into vertex form (i.e., complete the square).|
1. 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.
2. 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.
3. 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!
4. 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!
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. 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!
7. 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.
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