Transformations with Quadratic Functions

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Objective

SWBAT translate a quadratic function by re-writing the original equation.

Big Idea

Students explore transformations of quadratic functions through this investigation.

Lesson Author

James Bialasik

Amherst, NY

Grade Level

Ninth grade

Subjects

Math

Algebra

Transformations (Geom)

quadratic functions

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-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.

MP7

Look for and make use of structure.

Warm Up

10 minutes

The three slides in vertex_quick_review provide a brief warmup to today's lessons. I ask students to work with their partners. Since these are review tasks, I plan to touch base with students who have been struggling to master this material.

As students finish their work, I will call on volunteers to post answers on the board so that we can quickly review answers.