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# The Quadratic Formula-Day 1

Lesson 11 of 21

## Objective: SWBAT solve a quadratic equation using the quadratic formula

#### Warm Up

*5 min*

I will ask my students to complete this warm up with a partner:

Quadratic_Formula_Day 1_Launch.

The purpose of today's lesson is to learn how to solve quadratic equations using the quadratic formula. As the launch indicates, we will pursue this goal while making connections to the two methods that students have already learned: solving by factoring and by completing the square.

As students are finishing their work on the launch problems, I will have two students post answers on the board. I will choose one student demonstrate how to solve by factoring and the other solve by completing the square.

As other students finish, I will encourage them to review the work that is posted to make sure that it makes sense and to formulate a question if it does not. I may also ask students who are done to graph the associated function, f(x)=x^2+8x+12, to see that the roots match the solutions (MP5).

I plan to leave the student answers posted on the board to refer to during the direct instruction portion of the lesson.

#### Resources

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#### Independent Practice

*5 min*

I now provide students the opportunity to practice using the Quadratic Formula while working with their partners. Before students begin working on Quadratic_Formula_Day 1_Independent, I will ask them to determine if each of these equations can be solved by factoring. Then, I remind students that this can serve as a check for the solutions that thy derive using the Quadratic Formula. When students finish, I will encourage them to graph the associated functions in order to view a different representation of the roots.

On the Slide 2, I give students a problem that students will see as difficult to solve via factoring or completing the square. I encourage students to think about whether the Quadratic Formula will be the best option. I remind students that the Quadratic Formula will ALWAYS work to solve a quadratic equation that has real solutions. So, this can be a "go to" method that students will always want to remember.

#### Resources

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#### Closure

*5 min*

Quadratic_Formula_Day 1_Exit is a formative assessment of student understanding of the past several days of new material. The tasks encourage students to apply three different methods for solving a Quadratic Equations.

In Question #3, I want to see how they will choose an appropriate method from the three. I do not expect all students demonstrate mastery on this Ticket out the Door. At this point, their learning is still fairly new. I know that many students will need more experience in order to become adept at applying each of these methods. Today's closing activity is a checkpoint for me. It will help me to determine the needs of the students in the class.

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Hi James,

I have been modeling my lessons for our Quadratics unit off of yours for the past week. Thank you for posting them!! My class is actually Algebra for 7th/8th grade students in Middle School so we move a little quicker since it's an advanced course. I have enjoyed how your lessons encourage the students to discover the concepts versus just telling them the facts. I am wondering if/when you derive the Quadratic formula? (Maybe it's in a later lesson I haven't read yet...?). Thanks!

| 2 years ago | Reply

Hi James. I am planning on using your quadratic formula lesson tomorrow. I haven't taught my kids completing the square, as I believe a combination of factoring and the quadratic formula should be sufficient to address any quadratic equation. I'll let you know how the lesson goes! Thanks.

| 3 years ago | Reply*expand comments*

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- LESSON 1: Overview of Quadratics-Essential Vocabulary
- LESSON 2: Quadratic Functions and Roots
- LESSON 3: Equations involving Factored Expressions
- LESSON 4: Solving Quadratics by Factoring-Day 1
- LESSON 5: Solving Quadratics by Factoring-Day 2
- LESSON 6: Applications of Quadratics Day 1
- LESSON 7: Simplifying Radical Expressions
- LESSON 8: Solving Quadratic Equations with Perfect Squares
- LESSON 9: Completing the Square Day 1
- LESSON 10: Irrational Zeros of Quadratic Functions
- LESSON 11: The Quadratic Formula-Day 1
- LESSON 12: Comparing the Three Methods of Solving Quadratics
- LESSON 13: Three Methods of Solving Quadratics and Word Problems
- LESSON 14: Identifying Roots and Critical Points-Need to Edit
- LESSON 15: Graphing Quadratic Functions Day 1
- LESSON 16: Key Features of Quadratic Functions
- LESSON 17: Sketching Polynomial Functions
- LESSON 18: Vertex Form of a Quadratic Function
- LESSON 19: Transformations with Quadratic Functions
- LESSON 20: Modeling With Quadratic Functions
- LESSON 21: Projectile Problems & Review