About This Chapter
Standard: Factor a quadratic expression to reveal the zeros of the function it defines. ( CCSS.Math.Content.HSA-SSE.B.3a)
Standard: Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. (CCSS.Math.Content.HSA-SSE.B.3b)
Standard: Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)^2 = q that has the same solutions. Derive the quadratic formula from this form. (CCSS.Math.Content.HSA-REI.B.4a)
Standard: Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. (CCSS.Math.Content.HSA-REI.B.4b)
About This Chapter
If you understand the intricacies of quadratic equations you will be able to solve ones that aren't in standard form or have a side that is a perfect square. By completing this chapter, you should also know how to change a quadratic equation's form and solve a quadratic equation through factoring concepts.
Lessons in these standards cover concepts such as:
- Defining what a quadratic equation is
- Explaining how to factor a quadratic equation
- Solving quadratic equations when one side is a perfect square
- Changing a quadratic equation's form by completing the square
- Factoring to solve a quadratic equation
- Solving quadratic equations that aren't in standard form
- Finding the zeros for quadratic expressions
Students who mastered these standards are able to explain what the quadratic equation is. Depending on the information given, you will be able to solve quadratic equations in various circumstances. Throughout high school and college, you will understand how to break down quadratic equations to their simple factors. If you're running your own business, you can also apply these concepts when trying to figure out when your company will start making money.
How to Use These Lessons in Your Classroom
The following are some tips on how you can incorporate these lessons on quadratics into your curriculum to help meet the common core standards:
Factoring Quadratic Equation Lessons
Have your students watch the video lessons that focus on factoring quadratic equations. Develop a worksheet and have the students solve the problems by FOILing in reverse. Include polynomial problems that have a non-one leading coefficient. Spend time explaining each answer through step-by-step processes.
Completing the Square Lessons
Create and pass out a 'completing the square' worksheet. Take some time during class to watch our completing the square video lesson. Instruct the students to change standard form quadratic equations into vertex form quadratic equations. After the students complete the worksheet, demonstrate how to read the results and represent the results as a parabola on a graph.
Solving Quadratic Equations with the Quadratic Formula Lessons
Come up with a worksheet that contains non-factorable quadratic equations. After watching most of the quadratic equation video lessons, pass out the worksheet and have the students try to solve the equations. After a few minutes survey for results and show the video explaining how to solve quadratic equations with the quadratic formula. Replicate some worksheet equations on the chalkboard and call on students to the chalkboard to solve the equations. Provide guidance if they appear to be struggling.
1. What is a Quadratic Equation? - Definition & Examples
You might be surprised to learn that quadratic equations are an important part of the world we live in. We sometimes even make use of them for our entertainment! Watch this video lesson to learn more about these equations.
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. 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!
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. 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!
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 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 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.
9. 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 Common Core Math - Algebra: High School Standards course
- Common Core HS Algebra: Algebraic Expressions
- Common Core HS Algebra: Linear Equations
- Common Core HS Algebra: Linear Inequalities
- Common Core HS Algebra: Exponents and Exponential Functions
- Common Core HS Algebra: Polynomials
- Common Core HS Algebra: Rational and Radical Expressions and Equations
- Common Core HS Algebra: Systems of Equations
- Common Core HS Algebra: Matrices
- Common Core HS Algebra: Sequences and Series
- Understanding Common Core Standards