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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. √( ) ( )( )
( )
√