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# Interpreting and Graphing Quadratic Functions

Lesson 2 of 13

## Objective: SWBAT interpret graphs and tables and sketch graphs for quadratic functions. SWBAT relate the domain of a quadratic function to its graph, and interpret the domain in terms of the context.

## Big Idea: Students interpret key features of quadratics in real-life contexts to see the value of modeling and power of quadratics!

*90 minutes*

After yesterday's Introduction to Quadratic Functions, for homework I asked students to identify three examples of quadratic functions in real life and to explain why each example was a quadratic. Today's **Entry Ticket** provides time for students to share their lists and discuss the examples with each other. I view this activity as an opportunity to develop vocabulary and conceptual understanding.

- Students with prior understanding of quadratics can use this Warmup to practice their academic conversation skills by sharing their knowledge.
- Students who are unfamiliar with quadratics can hear their classmates explain some ideas and observations around quadratic functions and parabolas.

The entry ticket specifically asks students to identify the domain of each example, and relate the domain to the relationship it describes. This part of the entry ticket targets CCSS HSF.IF.B.5**. **

During this opening, I expect my students will converse with each other actively. As they do, I will make my way around the class checking for student understanding. I have in mind the students who struggled with yesterday's Exit Ticket and I will make sure to visit them first.

After students complete the Entry Ticket I will review the Agenda Board covering the learning and language objectives, plan, and homework. Today, I will ask students if they have anything else they want to include on the agenda. I do this from time-to-time to provide an opportunity to give students increased agency and ownership for their own learning.

If, in the case a student brings up an inappropriate idea for the agenda I ask the class for their input on whether or not that should be included – we use the class objectives and essential question as a decision making guide as to whether or not the proposed agenda item is relevant or not.

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In this section, I present new content to the class using **Interpreting and Graphing Quadratic Functions**. I ask students to actively take notes on the material, preferably in two-column form. I also provide students with a **Graphic Organizer** to help them process the information and organize their notes. From experience, I know that they will benefit from using this resource as a reference for graphing parabolas.

The presentation focuses on the interpretation of three key features of quadratic functions: concavity, vertices and intercepts. This section of the presentation directly connects to the standards **HSF-IF.B.4** and **HSF-IF-C.7a**. Each section of the presentation includes practice prompts.

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In this section of the lesson, I have students grapple with the **Group Work: Home Depot Problem**. The problem provides an opportunity for students to engage in several mathematical practices (**MP1, MP2, MP3, MP4)**. I designed this problem so that there was not one clear answer. I will encourage my students interpret the function in a way that makes sense to them and then model the situation. In the end, I want each group to generate their own justification for choosing a particular length of fence.

I really like the Rule of 4 Link sheet that is the second page of the **Group Work: Home Depot Problem**. I adapted this sheet for the Home Depot problem from an instructional unit from the Massachusetts Department of Elementary and Secondary Education (Reasoning with Equations Algebra I unit found at http://www.doe.mass.edu/candi/model/files.html). The Rule of 4 template helps students see the connections between different ways to represent functions, generally speaking. More specifically to this problem, I have found that having students work with quadratics in multiple representations at the same time helps differentiate instruction and gives students more entry points to understanding major concepts and structures of quadratic functions and equations.

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To close this lesson, I have each group complete the **Exit Ticket/Homework: Interpreting and Graphing Quadratic Functions** to organize and elaborate on their response to the Home Depot group problem from the previous section. I encourage students to focus on the area of providing examples/evidence to support their ideas. This prompt reflect my effort to focus on one of the five main skills of academic conversations during each unit in my algebra curriculum.

During this closing activity my students each have a copy of the Idea Organizer. They work on completing the template using their group's notes from the lesson. With 5 minutes before the end of the lesson, I assess where the class as a whole is on the Idea Organizer. If necessary, I will assign completing the Idea Organizer as homework.

If students have, for the most part, completed the task, then for homework I ask students to write a 1-2 paragraph written response based on the Idea Organizer. That way I am giving students a chance to practice their writing skills and also review the concepts from class with a high level of support (organized notes and Idea Organizer from a problem that already has been solved as a group).

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- UNIT 1: Thinking Like a Mathematician: Modeling with Functions
- UNIT 2: Its Not Always a Straight Answer: Linear Equations and Inequalities in 1 Variable
- UNIT 3: Everything is Relative: Linear Functions
- UNIT 4: Making Informed Decisions with Systems of Equations
- UNIT 5: Exponential Functions
- UNIT 6: Operations on Polynomials
- UNIT 7: Interpret and Build Quadratic Functions and Equations
- UNIT 8: Our City Statistics: Who We Are and Where We are Going

- LESSON 1: Introduction to Quadratic Functions
- LESSON 2: Interpreting and Graphing Quadratic Functions
- LESSON 3: Rate of Change & Comparing Representations of Quadratic Functions
- LESSON 4: Rearranging and Graphing Quadratics
- LESSON 5: Graphing Functions: Lines, Quadratics, Square and Cube Roots (and Absolute Values)
- LESSON 6: Building Quadratic Functions: f(x), kf(x) and f(kx)
- LESSON 7: Factoring and Completing the Square to Find Zeros
- LESSON 8: Forming Quadratics: Math Assessment Project Classroom Challenge
- LESSON 9: The Three Musketeers: Simplifying the Quadratic Formula
- LESSON 10: Quadratic Quandaries: Modeling with Quadratic Functions
- LESSON 11: Performance Task: Pulling It Together with Quadratics
- LESSON 12: Study Session for Unit Test on Quadratics
- LESSON 13: Unit Assessment: Quadratic Functions and Equations