About This Chapter
Factoring and Graphing Quadratic Equations - Chapter Summary and Learning Objectives
Instructors in this chapter can teach you the ins and outs of quadratic equations and their graphs. Video lessons cover steps for multiplying binomials, factoring, and completing the square so you can solve these types of equations regardless of their leading coefficient or form. This chapter is designed to help you:
- Identify a parabola's various points and forms
- Employ visual methods and the FOIL acronym to multiply binomials
- Use factoring and the quadratic formula to solve quadratic equations
- Convert quadratic equations into vertex and standard forms
|What Is a Parabola?||Find examples of parabolas in everyday life and learn to identify points, such as the vertex, maximum, intercept, root, and axis of symmetry.|
|Parabolas in Standard, Intercept, and Vertex Form||Explore three different forms of parabolas and learn how to interpret each one's value.|
|What Is a Function? - Applying the Vertical Line Test||Use the vertical line test to determine which graphs are functions.|
|Multiplying Binomials Using FOIL and the Area Method||Examine methods for multiplying algebraic expressions with two terms.|
|Multiplying Binomials Using FOIL and the Area Method: Practice Problems||Practice using area and FOIL methods to multiply binomials. Find out how to multiply two conjugates.|
|How to Factor Quadratic Equations: FOIL in Reverse||Learn how to break up quadratic equations into separate binomials.|
|Factoring Quadratic Equations: Polynomial Problems with a Non-1 Leading Coefficient||Get the hang of factoring quadratic equations with a leading coefficient greater than 1.|
|How to Complete the Square||View steps for converting a quadratic equation into vertex form.|
|Completing the Square Practice Problems||Review the processes involved in completing the square through examples and practice problems.|
|How to Solve a Quadratic Equation by Factoring||Discover uses of the product property and learn how to solve a quadratic equation by factoring.|
|How to Use the Quadratic Formula to Solve a Quadratic Equation||Find out how to solve quadratic equations using the quadratic formula and the correct order of operations.|
|How to Solve Quadratics That Are Not in Standard Form||Use algebra to convert a quadratic equation into standard form.|
|Graphing Circles: Identifying the Formula, Center and Radius||Learn how to find a circle's center and radius using the graph of a circle in standard form.|
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. What is a Function? - Applying the Vertical Line Test
Equations come in all shapes and sizes. Trying to determine which equations are functions can be difficult. You can apply the vertical line test to a graph to quickly tell whether or not it is a function.
4. 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.
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. 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.
8. 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!
9. 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!
10. 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.
11. 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.
12. Graphing Circles: Identifying the Formula, Center and Radius
Discover how to graph circles by finding key information like the center and radius. Identify circles by simply looking at the formula, and vice versa.
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