About This Chapter
Who's it for?
This unit of our High School Trigonometry Homeschool Curriculum course will benefit any student who is trying to learn about quadratic functions. There is no faster or easier way to learn about quadratics. Among those who would benefit are:
- Students who require an efficient, self-paced course of study to learn about the FOIL method of factoring, parabolas, quadratic inequalities and the practical applications of quadratic functions.
- Homeschool parents looking to spend less time preparing lessons and more time teaching.
- Homeschool parents who need a math curriculum that appeals to multiple learning types (visual or auditory).
- Gifted students and students with learning differences.
How it works:
- Students watch a short, fun video lesson that covers a specific unit topic.
- Students and parents can refer to the video transcripts to reinforce learning.
- Short quizzes and a Quadratic Functions unit exam confirm understanding or identify any topics that require review.
Quadratic Functions Unit Objectives:
- Define a parabola.
- Become familiar with parabolas in intercept, standard and vortex forms.
- Factor and solve quadratic equations.
- Find the minimum and maximum value of a parabola by completing the square.
- Graph a quadratic inequality or system of quadratic inequalities.
- Understand how quadratic functions are used to solve problems or model data.
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. 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.
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 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.
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 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!
8. How to Solve Quadratics with Complex Numbers as the Solution
When you solve a quadratic equation with the quadratic formula and get a negative on the inside of the square root, what do you do? The short answer is that you use an imaginary number. For the longer, more helpful answer, check out this lesson!
9. Graphing & Solving Quadratic Inequalities: Examples & Process
When you finish watching this video lesson, you will be able to graph and solve your own quadratic inequality. Learn what steps you need to take and what to watch for.
10. Graphing a System of Quadratic Inequalities: Examples & Process
What is a system of quadratic inequalities? What are the steps to graphing them? Find the answers to these questions by watching this video lesson. When you finish, you will be able to graph these yourself.
11. Applying Quadratic Functions to Motion Under Gravity & Simple Optimization Problems
Quadratic functions are very useful in the real world. Watch this video lesson and learn how these functions are used to model real world events such as a falling ball.
12. 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 High School Trigonometry: Homeschool Curriculum course
- Types of Real Numbers: Homeschool Curriculum
- Working with Linear Equations: Homeschool Curriculum
- Graphing Inequalities: Homeschool Curriculum
- Absolute Value Equations: Homeschool Curriculum
- Complex Numbers: Homeschool Curriculum
- Using Systems of Linear Equations: Homeschool Curriculum
- Mathematical Modeling: Homeschool Curriculum
- Introduction to Quadratics: Homeschool Curriculum
- Coordinate Geometry: Homeschool Curriculum
- Functions for Trigonometry: Homeschool Curriculum
- Function Operations: Homeschool Curriculum
- Graph Symmetry: Homeschool Curriculum
- Graphing with Functions: Homeschool Curriculum
- Polynomial Functions Basics: Homeschool Curriculum
- Higher-Degree Polynomial Functions: Homeschool Curriculum
- Difference Quotients: Homeschool Curriculum
- Function Graphs: Homeschool Curriculum
- Exponential Functions: Homeschool Curriculum
- Trigonometric Functions: Homeschool Curriculum
- Triangle Trigonometry: Homeschool Curriculum
- Trigonometric Graphs: Homeschool Curriculum
- Solving Trigonometric Equations: Homeschool Curriculum
- Trigonometric Identities: Homeschool Curriculum
- Trigonometric Applications: Homeschool Curriculum
- Analytic Geometry: Homeschool Curriculum
- Vectors, Matrices & Determinants: Homeschool Curriculum
- Polar Coordinates: Homeschool Curriculum
- Circular Arcs, Circles & Angles: Homeschool Curriculum