Rhonda Leichliter ROGERS HIGH SCHOOL, ROGERS, AR
Algebra I : Unit #8 - Quadratic Functions : Lesson #8

Solving Quadratic Functions Using the Quadratic Formula

Objective: SWBAT solve a Quadratic Equation using the Quadratic Formula with and without a calculator.
Standards: HSA-SSE.A.1 HSA-SSE.A.1a HSA-REI.B.4 HSF-IF.C.7a MP1 MP3 MP4 MP5
Subject(s): Math
60 minutes
1 Warm Up - 10 minutes

In this Warm Up, I provide students with a Quadratic Equation that I want them to solve using a calculator.  Then I have students solve the same Quadratic Equation without a calculator to verify that their solution is correct (MP3).  I expect that many of the students answers will not be the same.  The purpose of this lesson is for students to develop a method that consistently gives them correct solutions to a Quadratic Equation when using the Quadratic Formula.

It is a common mistake for students to get the incorrect answer when using a calculator.  The most common reason is that students do not know how to enter the formula correctly into the calculator with correct groupings.  

So after the students complete the Warm Up, I demonstrate one way that a student can enter the formula into the calculator.  I also emphasize to students to rewrite the equation with the parentheses in the places that they are going to enter them into the calculator. By writing and entering the Parentheses the same way, students should be more successful.  I demonstrate using the calculator to solve the Quadratic Formula in the video below.

 Link

 

Students may choose not to use the calculator as they work through today's lesson.  It is their choice, but I want them to be consistent at getting the correct solutions when using the Quadratic Formula.  Students should also recognize that the calculator is a more efficient way to solve the Quadratic Formula to save time if done correctly.

Students should become successful with using the Quadratic Formula with Practice and by Verifying their answers.  Students may verify their answers themselves as in the Warm Up, with checks by the teacher, or by working with their table partner(s).

Importance of Deriving the Quadratic Formula by Completing the Square
Connection to Prior Knowledge

I think it is important to help students see the connection between deriving the Quadratic Formula by completing the square.  By using students' prior knowledge of completing the square, it is amazing to some students how the Quadratic Formula is formed.  Below is a video from Khan Academy modeling the proof:

Link

2 Partner Work - 30 minutes

After reviewing the Warm Up with students, I hand each pair of students a set of Equations Cards, and a set of Solution Cards.  Students are to work with their table partner to determine the solutions for each equation.  Here is a Key to the Activity.  I already have table partners placed in homogeneous groups based on the ability of each student when working with Quadratic Functions previously in this unit.

I accessed the Equation Cards from the following website:

http://www.cpalms.org/Public/PreviewResource/Preview/51208 (last accessed 7-01-15)

I created my own Solution Cards.  The task for students on the website above was to determine the best method to apply to solve each Quadratic Equation.  For the purposes of this lesson, I wanted students to solve all of the Quadratic Equations using the Quadratic Formula.  

Students did recognize that some Quadratic Equations were easier to solve using methods of factoring or finding the square root previously learned.  However, I encouraged students to use those methods to verify their solutions, but to solve using the Quadratic Formula.

By having students solve all of the Quadratic Equations using the Quadratic Formula, it provides them with practice on cases in which b or c are equal to zero.  It helps students to see that the Quadratic Formula is used to solve any Quadratic Equation.  

After providing students with about 20 to 25 minutes to work on the collaborative Partner Activity, I randomly call on students to provide a solution to an equation that their group had identified.  All of the Partners may not complete all of the matches, but I still move on for them to compare their answers and reasons with their peers.  If any groups disagree, I have a student work the problem on the board to verify which is the correct answer.

 

 

3 Exit Slip - 10 minutes

After checking students answers on the Partner Activity, I hand each student an Exit Slip.  Students will need to refer to the Quadratic Equations used in the Partner Activity for the Exit Slip.  So, I post the Quadratic Equation Cards on the board for students to view while answering the questions on the Exit Slip.

Students are to select a Quadratic Equation that fits each of the following categories:

1.  Use the Quadratic Formula Only to Solve

2.  Factoring is an easier method to use to Solve

3.  Using the Square Root method is an easier method to use to Solve

After providing about five minutes for students to complete the questions on the Exit Slip, I collect them to share under the document camera.  I do not show names, and it provides a good closure at the end of the lesson.  It provides an opportunity for me to review with the students.

Students should understand by the end of this lesson that the Quadratic Formula can be used to solve any Quadratic Equation with real or complex roots.  However, this Exit Slip also provides students with examples of when the Quadratic Formula is the best option to solve a Quadratic Equation.  It also shows students when other methods may be more efficient depending on the problem.