About This Chapter
Quadratic Functions & Polynomials - Chapter Summary
Use the lessons in this chapter to find out what, exactly, a parabola is. Learn how to manipulate the direction of these functions by writing quadratic equations in the standard, intercept and vertex forms, and discover methods for maintaining the correct order of operations when multiplying binomials and factoring quadratic expressions.
Once you've mastered the basics, learn the steps for factoring a trinomial into a square binomial. You can also practice using the quadratic formula and study techniques for solving quadratic equations that aren't in standard form. Additional lessons show you how to graph a quadratic equation to locate the x- and y-intercepts. There are also tips for finding the maxima and minima of a quadratic function, determining the end behavior of a polynomial and graphing monomials. A lesson on factoring quadratic functions to find zeros rounds out the chapter, which is designed to teach you the following main topics:
- Multiplying binomials
- Factoring quadratic equations
- Using the quadratic formula
- Graphing monomials and polynomials
Our video lessons put the expertise of experienced instructors at your disposal. Watch them model the steps for solving quadratic equations and use the corresponding lesson transcripts to peruse the examples and explanations provided. If you'd like to try your hand at solving some of these problems, there are also quizzes to help you assess your comprehension of each lesson's content.
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. 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. 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.
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Other chapters within the TExES Mathematics 7-12: Practice and Study Guide course
- Real Numbers
- Mathematical Models
- Complex Numbers & the Complex Plane
- Number Theory
- Number Patterns
- Functions and Graphs
- Linear Functions
- Evaluating Piecewise & Composite Functions
- Rational and Radical Functions
- Inequalities and Absolute Values
- Exponentials & Logs
- The Unit Circle
- Trigonometric Functions
- Using a Scientific Calculator for Calculus
- Limits of Functions
- Understanding Rate of Change
- Calculating Derivatives of Functions
- Derivatives and Graphs
- Optimization in Calculus
- Definite Integrals and Sums
- Indefinite Integrals in Calculus
- Integration Applications in Calculus
- Working with Measurement
- Geometrical Figures
- Introduction to Proofs and Constructions
- Congruence and Similarity
- Conic Sections
- Coordinate Geometry
- Finding Volume, Area & Perimeter
- Descriptive Statistics
- Sampling in Statistics
- Normal Distribution in Statistics
- Inference About a Mean
- Categorical Data
- Regression and Correlation
- Finding Probability
- Probability Distributions and Statistical Inference
- Experiments and Surveys
- Teaching Strategies & Activities for the Math Classroom
- Differentiated Instructional Strategies for the Math Classroom
- Using Student Assessments in the Math Classroom