About This Chapter
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Anyone who needs help learning or mastering precalculus material will benefit from taking this course. There is no faster or easier way to learn precalculus. Among those who would benefit are:
- Students who have fallen behind in understanding and working with factoring and graphing quadratic equations
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning math (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about factoring and graphing quadratic equations
- Students who struggle to understand their teachers
- Students who attend schools without extra math learning resources
How it works:
- Find videos in our course that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the Factoring and Graphing Quadratic Equations chapter exam.
Why it works:
- Study Efficiently: Skip what you know, review what you don't.
- Retain What You Learn: Engaging animations and real-life examples make topics easy to grasp.
- Be Ready on Test Day: Use the Factoring and Graphing Quadratic Equations chapter exam to be prepared.
- Get Extra Support: Ask our subject-matter experts any factoring and graphing quadratic equations question. They're here to help!
- Study With Flexibility: Watch videos on any web-ready device.
Students will review:
In this chapter, you'll find the answers to questions including:
- What is the definition of a parabola?
- How are parabolas expressed in standard, intercept and vertex form?
- How is the vertical line test used to determine functions?
- What are the area and FOIL methods for multiplying binomials?
- How do I factor and solve quadratic equations, including non-standard expressions?
- What is meant by 'completing the square' in precalculus?
- How do I graph circles?
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.
13. Factoring Quadratic Expressions: Examples & Concepts
In this lesson, you will learn the trick to factoring quadratic expressions. Also, because not all quadratics can be factored, you can discover how to identify the expressions that you can't simplify.
14. Reflectional Symmetry: Definition & Examples
Reflectional symmetry can be found in geometric figures, math, nature and the man-made world. In this lesson, we'll explore the characteristics that define reflectional symmetry, as well as some everyday examples.
15. Trinomials: Factoring, Solving & Examples
Trinomials can have different leading coefficients and therefore, have to be factored differently. Learn how to factor and solve any trinomial. Then, test your knowledge with a quiz.
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Other chapters within the Precalculus: Help and Review course
- Functions in Precalculus: Help and Review
- Evaluating Exponential and Logarithmic Functions: Help and Review
- Inequalities in Precalculus: Help and Review
- Foundations and Linear Equations in Precalculus: Help and Review
- Graphing and Rational Equations: Help and Review
- Exponents and Polynomials in Precalculus: Help and Review
- Piecewise and Composite Functions: Help and Review
- Geometry and Trigonometry: Help and Review
- Using Scientific Calculators: Help and Review
- Trigonometry: Help and Review