The Quadratic Formula

Target Audience: Introduction to Algebra Class at Bel Air High School, 90 minutes

Lesson Topic: The Quadratic Formula

NCTM Standards: (Algebra Standard for Grades 9-12) Understand relations and functions and

select, convert flexibly among, and use various representations for them.

Maryland State Curriculum: (A.SSE.3) Choose and produce an equivalent form of an

expression to reveal and explain properties of the quantity represented by the expression.

Common Core State Standards: (High School Algebra) Solve quadratic equations by

inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula

and factoring, as appropriate to the initial form of the equation.

Before the Lesson:

Objective: SWBAT

1. Recite the quadratic formula

2. Use the quadratic formula to solve the solutions of quadratic equations

Prerequisite Knowledge: Students know what a quadratic equation is, the shape of a graph of a

quadratic equation, and how to calculate the discriminant. Students can use the discriminant

value to predict how many solutions the quadratic equation has.

Materials: Drill, Quadratic Formula Notes, Quadratic Formula Classwork, The Quadratic

Formula Powerpoint, Exit Ticket, and calculator

During the Lesson:

Warm-up

Students will complete a drill on quadratic equations that assesses student’s prerequisite

knowledge. The drill is attached.

At this point the teacher will begin the actual lesson using the attached Quadratic Formula

Powerpoint. The teacher should pass out the Quadratic Formula Notes ditto.

Engagement:

The teacher will briefly review quadratic equation form and the shape of it’s graph with

the students. The teacher and students will discuss where they see parabolas in real life. ie:

arches, roller coasters, basketball shots, etc.

Exploration:

The teacher will introduce the first 2 steps to solving a quadratic equation:

1. Set the equation equal to zero

2. Identify a, b, and c

Students will practice each step with the examples from the Powerpoint.

Explanation:

Using the example on the Quadratic Formula Notes ditto: f(x) = x2 + 3x – 4 the teacher

will introduce the last 2 steps to solving a quadratic equation:

3. Write the quadratic formula

To help students remember the formula the teacher will play the following video:

http://www.youtube.com/watch?v=O8ezDEk3qCg

The teacher will write the quadratic formula on the dry erase board as the video is playing. Once

the video has played, the teacher will sing the song and then the students will sing the song. The

class should sing the song all together

4. Plug & Chug

The class should solve the quadratic equation by plugging the a, b, and c values into the

equation. This can be done using a calculator.

Extension: The class will be divided into 3 groups; each group will be assigned a problem to solve

together. The problem will come from the Quadratic Formula Classwork. After the groups

have solved the problem, one member will be asked to present and described the steps they took

to solve the problem. Students should pay attention and take notes from the different groups.

Evaluation:

The students will be asked to complete an exit ticket. The exit ticket is attached.

Drill- quadratic equations (answers in red)

3-1-12

1. What makes linear equations and quadratic equations different?

Linear equations have a degree of 1 and form a straight line

Quadratic equations have a degree of 2 and for a parabola

Evaluate each quadratic equation for the given value of x. Show all work.

2. ( ) ( )

5

3. ( ) ( )

-15

4. ( )

241

The Quadratic Formula: NOTES

Review:

Quadratic function form: _______________

Name and picture of graph: _______________

Examples of parabolas in real-life:

How do we solve for x in a quadratic function? _______________

Step 1: _______________

Step 2: _______________

Step 3: _______________

Step 4: _______________

Example: x2 + 3x – 4 = f(x) Use the quadratic formula to solve for x.

The Quadratic Formula

The Quadratic Formula: CLASSWORK

Use the quadratic formula to solve for x in the following problems. Show all work.

1. 2x2 – 6x – 5 = f(x)

2. x2 + 2x = f(x)

3. f(x) = -2x2 +x + 3

Exit Ticket- quadratic formula (answer in red) Name: _________________

Solve the following using the quadratic equation. Show all 4 steps discussed in class. (if

necessary round your answer to the nearest thousandth)

( )

1.

2.

3. √

4. √( ) ( )( )

( )

√