Objective

Warm-Up

Solving Problems using 1 Method

Multiple Methods to Solve Problems with Quadratic Functions

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Objective

SWBAT use different methods to determine missing information about quadratic functions.

Big Idea

Give students problems that allow for multiple points of entry and let them use lots of time and technology to develop their own methods to solve them--after several days, you will be excited to see all the different methods they come up with!

Lesson Author

Hilary Yamtich

Oakland, CA

Grade Level

Eleventh grade

Twelfth grade

Subjects

Math

Algebra

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.

Warm-Up

40 minutes

Solving Problems using 1 Method

30 minutes

The idea is for students to work on these same problems two days in a row. Today, they can just use whatever method they prefer, and make sure they master it and can fully explain how it works.

I name each method on the board:

1) x-intercepts

2) Product of Linear Factors

3) Vertex Form

Even though we have never really explained these methods, students are usually able to choose the name of the method they are using. I ask them to make sure that they can identify their preferred method and explain how it works. I tell them that tomorrow they will be responsible for teaching their method to another person, and will need to master another method to solve each of the 3 problems.

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