Solving Quadratic Functions Algebraically and by using Square Roots

2 Class Periods– 180 minutes DAY 1

Instruction on Solving Quadratic Functions Algebraically–30 minutes

Pose the question “If a times b equals zero, what do we know about a and b?” Discuss students’ answers as a class. Introduce the Zero Product Property (If ab = 0 then a = 0 or b = 0). Have students write the property in their notes. Introduce a new problem.

(x)(x + 5) = 0 Ask students if we can apply the Zero Product Property. Have students who believe it is possible stand up. Ask one of the standing students about their opinion. Confirm that anytime two factors equal zero, you can use the property. In the case above, you know that one of the factors must equal zero. So either x = 0 or x + 5

= 0. For x + 5 = 0, you solve for x. You get two solutions of x = 0 or x = -5. As a class, practice solving several equations with the Zero Product Property. Have students try several problems independently in their notes, and go over these problems as a class.

Next, ask students if you can solve 0 = x² + 5x + 6 with the Zero Product Property.

Have each student come up with an answer and rationale and share it with their 1^st base teammate. After teammates have shared, ask for volunteers to share their opinions with the whole class. Discuss these opinions. Inform students that you can use the Zero Product Property, but first you must factor the problem. Remind students of the reverse FOIL method in unit eight where we learned how to factor a

polynomial by undoing the FOIL method.

0 = x² + 5x + 6 needs to become

0 = ( )( )

First we label the original equation. 0 = x² + 5x + 6 F O + I L

Then, we ask what two factors make x²? Those go first in the parenthesis.

What two numbers multiply to make 6 but add to make 5? Those go last in the parenthesis.

Now we can use the Zero Product Property to find the solutions. As a class, practice factoring and then solving several quadratic equations. Have students attempt several problems independently in their notes, and go over these problems as a class.

*Section I: Tiered Assignment–20 minutes

There are three versions of the Practice Makes Perfect- Solving Quadratics

assignment. Each version has the same format, the same amount of problems, and focuses on the same concepts and skills. The difference is that each of the versions is uniquely created to match different readiness levels. Version O is the original version of the assignment created for students at grade level readiness. Version A is designed for students above grade level readiness. Version B is for students below grade level readiness. Students will be given the version that best matches their readiness level.

Section I of this assignment focuses on solving quadratic functions by factoring and using the Zero Product Property. Students will work individually on each section of this assignment. After completing Section I, students can confer with their 3^rd base partners (who will have the same version because both students have similar readiness levels) on their answers.

Instruction on Solving Quadratic Functions by using Square Roots–25 minutes Pose the question “What is the square root of 25?” Have students write the answer down in their notes. Inform students that 5 is not the correct answer. Remind students that there are two square roots to any positive number. The square root of 25 is 5 and -5. Ask students what is the square root of zero? What is the square root of a negative number?

Inform students that we are going to be using our knowledge of square roots to solve quadratic equations. First we are going to refresh our memories by solving a few square roots problems. Solve the following problems as a class.

81 = x² 20 = x²

0 = x² -16 = x²

Have students practice several similar problems in their notes. Go over the answers as a class.

Now display the following problem on the board. 0 = x² – 100 Inform students that we can solve this problem using square roots, but there is something we must do first.

Ask for suggestions. Remind students that when solving an equation we must use reverse order of operations. In this case, we cannot undo the square before undoing the subtraction. Model how to solve this problem and several similar problems. Have students try a few individually in their notes. We will go over them as a class before moving to the next section of the tiered assignment.

*Section II: Tiered Assignment–15 minutes

Section II focuses on solving quadratic functions by using square roots. Problems ask students to take the square root of perfect squares, numbers that are not perfect squares, negative numbers, and zero. Students may again confer with their 3^rd base partners when finished.

*Anchor Activity– as time allows DAY 2

*Section III: Tiered Assignment–25 minutes

Section III features open-ended questions about solving quadratic functions. Students may also finish any incomplete sections during this time. When finished, students may again confer with their 3^rd base partners. Students may check their answers against the answer key on the front table when they are completely finished with all three sections.

*Anchor Activity– as time allows

*Student Self-Evaluation on Learning Objectives–10 minutes

Students will update their learning objective checklist and complete another self-evaluation. Students will be encouraged to consider all of the activities, assignments, and the assessment that they have completed so far in this unit.

*RAFT Writing Activity–55 minutes

Inform students that although they may never have dreamed of becoming a quadratic function, today they will get the chance. Introduce the RAFT writing activity as a creative opportunity to write from a new perspective to demonstrate knowledge about quadratic functions. Give students the RAFT writing activity and rubric. Go over the directions and the five options as a class. Ask for questions, and then let students

begin writing. If time allows, ask for student volunteers to share their RAFT writing with the class.

*Anchor Activity– as time allows