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# Choosing a Method to Find x-intercepts

Lesson 14 of 18

## Objective: SWBAT determine which method (graphing, vertex form, or factoring) is most appropriate for finding x-intercepts given a quadratic function. SWBAT find a quadratic for two given x-intercepts.

#### Opening

*7 min*

I start today’s lesson will begin with a **Curriculum Based Assessment** on factoring:

I use this CBA as a quiz or as a quick check-in to make sure students understand how to factor. I set the timer for five minutes on this CBA and let students work on any of the problems on the page. I only give page one of this pdf. After the timer goes off, I collect student work. I'll want to make sure to correct it before the next class so I can arrange for one-on-one or small group instruction for students who are still struggling.

**DIFFERENTIATION**: Students who are ready for more advanced factoring can work on Factoring 2, a more advanced set of tasks.

#### Resources

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#### Investigation

*45 min*

The point of today’s lesson is for students to tie some loose ends together and begin finishing the unit on Quadratics. Students will work together in small groups and I may discuss their results with them as they work or gather everyone together at the end class.

The first activity asks students to explain Which Method they would use to find the x-intercepts of a quadratic and why. They are also asked to explain why they chose that method. I will discuss this work as a whole group or in small groups as they finish when to use which method. I want to make sure students understand that the vertex method will always work for any quadratic.

The Find a Quadratic activity asks students to write equations for a quadratic function based on given x-intercepts. Students will then move on to Find a Quadratic. Students will be given x-intercepts and be asked to write a quadratic with those intercepts. I find some students will need help to write a function for three x-intercepts. I try to elicit from students that this will not be a quadratic and help them understand why.

Most students will write basic answers for their equations. For example, given the x-intercepts x = 3 and x = 2, most students will write y = (x – 3)(x – 2). I ask students ready for an extension to write this equation in standard form. I also try to elicit from students that this is not the only equation of a quadratic with these x-intercepts I try to elicit from students what some other equations might be that have the same x-intercepts. Students should realize that any value of *a* with the same equation will work.

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#### Closing

*8 min*

I give students time at the end of this lesson to reflect on their preferences for solving for x-intercepts. I ask them to write an exit ticket responding to the following prompt:

**Which method do you prefer to find the x-intercepts of a quadratic and why?**

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- UNIT 1: Introduction to Algebra: Focus on Problem Solving
- UNIT 2: Multiple Representations: Situations, Tables, Graphs, and Equations
- UNIT 3: Systems of Equations and Inequalities
- UNIT 4: Quadratics!
- UNIT 5: Data and Statistics
- UNIT 6: Arithmetic & Geometric Sequences
- UNIT 7: Functions

- LESSON 1: A Fireworks Display
- LESSON 2: Rabbit Run -- Day 1 of 2
- LESSON 3: Rabbit Run -- Day 2 of 2
- LESSON 4: Properties of Parabolas Day 1 of 2
- LESSON 5: Properties of Parabolas Day 2 of 2
- LESSON 6: Using an Area Model to Multiply Binomials
- LESSON 7: Vertex Form to Standard Form
- LESSON 8: Standard Form to Vertex Form Day 1 of 2
- LESSON 9: Standard Form to Vertex Form Day 2 of 2
- LESSON 10: Where Will the Rocket Land? Putting it all Together
- LESSON 11: Completing the Square Methods & Practice
- LESSON 12: Factoring Day 1 of 2
- LESSON 13: Factoring Day 2 of 2
- LESSON 14: Choosing a Method to Find x-intercepts
- LESSON 15: Quadratics Portfolio Day 1 of 3
- LESSON 16: Quadratics Portfolio Day 2 of 3
- LESSON 17: Quadratics Portfolio Day 3 of 3
- LESSON 18: Is It a Home Run?