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- Unit 1: Linear and Nonlinear Functions
- Unit 2: Piecewise Functions
- Unit 3: Absolute Value Functions and More Piecewise Functions
- Unit 4: Introduction to Quadratic Functions through Applications
- Unit 5: More Abstract Work with Quadratic Functions
- Unit 6: Rational Functions
- Unit 7: Polynomial Functions
- Unit 8: Exponential Functions
- Unit 9: Ferris Wheels
- Unit 10: Circles
- Unit 11: Radical Functions
- Unit 12: Cubic Functions

- LESSON 1: Investigating Profit with Products
- LESSON 2: More Profit Maximization Investigations
- LESSON 3: Profit Maximization Problems Workshop: Multiple Methods
- LESSON 4: Multiple Methods to Solve Problems with Quadratic Functions
- LESSON 5: More Multiple Methods to Solve Problems involving Quadratic Functions
- LESSON 6: 4-Column Quadratic Data Tables
- LESSON 7: More 4-Column Data Tables
- LESSON 8: Applying Data Tables to Word Problems
- LESSON 9: Profit Maximization and 4-Column Data Tables Review
- LESSON 10: Profit Maximization and 4-Column Data Tables Summative Assessment
- LESSON 11: Different Forms of Quadratic Functions
- LESSON 12: Quadratic Data Tables
- LESSON 13: Finding Vertices of Parabolas
- LESSON 14: Heights of Falling Objects
- LESSON 15: Profit Maximization
- LESSON 16: Quadratic Functions Review and Portfolio
- LESSON 17: Quadratic Functions Summative Assessment

Objective

Warm-Up

Investigation and New Learning

Closing

SWBAT use quadratic functions to solve profit maximization problems.

What happens to the number of customers as you increase the price of the item? How does this affect your profit?

Lesson Author

Hilary Yamtich

Oakland, CA

Grade Level

Eleventh grade

Twelfth grade

Subjects

Math

quadratic functions

Algebra

modeling

Function Operations and Inverses

Quadratic Equations

Standards

HSF-IF.B.4

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*

HSF-IF.C.7a

Graph linear and quadratic functions and show intercepts, maxima, and minima.

HSF-IF.C.8a

Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

HSF-BF.A.1

Write a function that describes a relationship between two quantities.*

HSF-BF.B.3

Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

MP1

Make sense of problems and persevere in solving them.

MP2

Reason abstractly and quantitatively.

MP3

Construct viable arguments and critique the reasoning of others.

MP4

Model with mathematics.

MP5

Use appropriate tools strategically.

MP6

Attend to precision.

MP7

Look for and make use of structure.

MP8

Look for and express regularity in repeated reasoning.

30 minutes

Proft Maximization Warm-Up.docx

30 minutes

Prom Ticket Problem.docx

Profit Maximization Investigation.docx

Profit Maximization Generalization.docx

Profit Maximization Problems.docx

10 minutes

Profit Maximization Exit Ticket.docx

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Lesson Author

Hilary Yamtich

Oakland, CA

Grade Level

Eleventh grade

Twelfth grade

Subjects

Time

70 Minutes