# Ch 4: Common Core HS Algebra: Quadratics

Discover informative lessons in high school algebra. These lessons meet the Common Core Mathematics standards for quadratics (CCSS.Math.Content.HSA-SSE.B.3a; CCSS.Math.Content.HSA-SSE.B.3b; CCSS.Math.Content.HSA-REI.B.4a; CCSS.Math.Content.HSA-REI.B.4b).

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)

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:

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.

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.

9 Lessons in Chapter 4: Common Core HS Algebra: Quadratics
Test your knowledge with a 30-question chapter practice test
Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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