The Quadratic Formula
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- Griffin Chambers
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1 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:
2 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) = x 2 + 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: 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.
3 Drill- quadratic equations (answers in red) 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. ( ) ( ) ( ) 241
4 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: The Quadratic Formula Step 2: Step 3: Step 4: Example: x 2 + 3x 4 = f(x) Use the quadratic formula to solve for x.
5 The Quadratic Formula: CLASSWORK Use the quadratic formula to solve for x in the following problems. Show all work. 1. 2x 2 6x 5 = f(x) 2. x 2 + 2x = f(x) 3. f(x) = -2x 2 +x + 3
6 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) 2. ( ) ( ) ( )( ) ( )
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