About This Chapter
How It Works:
- Find the lesson within this chapter that corresponds to what you're studying in the Quadratic Functions of the Form of f(x) = ax^2 + bx + c chapter of your textbook.
- Watch fun videos that cover the mathematical concepts you need to learn or review.
- Complete the quiz after finishing each video and text lesson to test your understanding.
- If you need additional help, review the lessons until you've mastered the material, or submit a question for one of our instructors.
You'll learn all of the mathematics topics covered in the textbook chapter, including:
- The FOIL and area method for multiplying binomials
- How to apply the FOIL method in reverse
- Factoring quadrating trinomials and perfect square trinomials
- Completing the square
- The quadratic formula and how it's used
- Quadratics and nonlinear systems
- How to model a given data set with quadratic functions
On Core Mathematics is a registered trademark of Houghton Mifflin Harcourt, which is not affiliated with Study.com.
1. 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.
2. 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.
3. 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.
4. 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.
5. Factoring Perfect Square Trinomials Practice Problems
A perfect square trinomial is a special form of trinomial that has a unique method for factoring it. We'll go over that method here and then cement it in your mind by working through a couple practice problems.
6. The Quadratic Formula: Definition & Example
Watch this video lesson to learn how you can use the quadratic formula to solve certain types of problems. Learn what kinds of equations you can solve using this formula as well as how easy it is to use this formula.
7. 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.
8. Solving Nonlinear Systems with a Quadratic & a Linear Equation
In this lesson, we'll learn how to solve non-linear systems with a quadratic and linear equation both algebraically and graphically. We'll also look at the different possible solutions for this type of system.
9. Using Quadratic Functions to Model a Given Data Set or Situation
Watch this video lesson to learn how quadratic functions are used to model situations and data gathered from real world scenarios. See how our function fits our data and situation well.
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Other chapters within the Harcourt On Core Mathematics - Algebra 1: Online Textbook Help course
- On Core Mathematics Algebra 1 Unit 1: Algebraic Modeling and Unit Analysis
- On Core Mathematics Algebra 1 Unit 2: Linear Equations and Inequalities
- On Core Mathematics Algebra 1 Unit 3: Systems of Equations and Inequalities
- On Core Mathematics Algebra 1 Unit 4: Linear Functions
- On Core Mathematics Algebra 1 Unit 5: Exponential Functions
- On Core Mathematics Algebra 1 Unit 6: Piecewise and Absolute Value Functions
- On Core Mathematics Algebra 1 Unit 7: Quadratic Functions of the Form of f(x) = a(x-h)^2 + k
- On Core Mathematics Algebra 1 Unit 9: Data Analysis