Algebra 2 5-9 Complete Lesson: Transforming Polynomial Functions

Last updated about 4 years ago

23 questions

Note from the author:

A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

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Algebra 2 5-9 Complete Lesson: Transforming Polynomial Functions

Algebra 2 5-9 Complete Lesson: Transforming Polynomial Functions

Solve It! The graph of the parent cubic function f(x) = x³ is shown in blue. The red graph is a transformation g of the parent function f. What is an equation for g?

Problem 1 Got It?

Problem 2 Got It?

Problem 3 Got It? What is a quartic function f(x) with only two real zeros, x = 0 and x = 6?

Problem 3 Got It? Reasoning: Does -f(x) have the same zeros? Explain.

Vocabulary: Is the function below an example of a power function?

Vocabulary: Explain your response above.

Error Analysis: Your friend says that he has found a way to transform the graph of the function below to obtain three real roots. Using the graph of the function, explain why this is impossible. You may use the embedded Desmos utility below to graph the function.

Compare and Contrast: How are the graphs of the two functions below alike? different? What transformation was used to get the second equation?You may use the embedded Desmos utility above to graph the functions.

Review Lesson 5-8: Create a table and plot the points on the coordinate plane. Find and graph a polynomial function that passes through all of the given points. Zoom and pan your graph to establish an appropriate viewing window.

Review Lesson 5-8: Create a table and plot the points on the coordinate plane. Find and graph a polynomial function that passes through all of the given points. Zoom and pan your graph to establish an appropriate viewing window.

Review Lesson 2-4: Graph the lines described below on the same coordinate plane. Zoom and pan your graph to establish an appropriate viewing window.

Review Lesson 2-1: Classify each relation.

Vocabulary Review: Identify the constant in the expression.

Vocabulary Review: Identify the expressions that do not contain a constant term. Select all that apply.

Use Your Vocabulary: Identify the translation, reflection, stretch, and compression of the word Algebra.

Key Concept: Identify the function(s) that are NOT Power Functions.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success

Solve It! The graph of the parent cubic function f(x) = x³ is shown in blue. The red graph is a transformation g of the parent function f. What is an equation for g?

Problem 1 Got It?

Problem 2 Got It?

Problem 3 Got It? What is a quartic function f(x) with only two real zeros, x = 0 and x = 6?

Problem 3 Got It? Reasoning: Does -f(x) have the same zeros? Explain.

Problem 4 Got It? Wind-Generated Power: The power P (in kilowatts) generated by a wind turbine varies directly as the cube of the wind speed v (in meters per second). A wind turbine generates 210 kW of power in a 12 mi/h wind. How much does this turbine generate in a 20 mi/h wind?

Vocabulary: Is the function below an example of a power function?

Vocabulary: Explain your response above.

Error Analysis: Your friend says that he has found a way to transform the graph of the function below to obtain three real roots. Using the graph of the function, explain why this is impossible. You may use the embedded Desmos utility below to graph the function.

Compare and Contrast: How are the graphs of the two functions below alike? different? What transformation was used to get the second equation?You may use the embedded Desmos utility above to graph the functions.

Review Lesson 5-8: Create a table and plot the points on the coordinate plane. Find and graph a polynomial function that passes through all of the given points. Zoom and pan your graph to establish an appropriate viewing window.

Review Lesson 5-8: Create a table and plot the points on the coordinate plane. Find and graph a polynomial function that passes through all of the given points. Zoom and pan your graph to establish an appropriate viewing window.

Review Lesson 2-4: Graph the lines described below on the same coordinate plane. Zoom and pan your graph to establish an appropriate viewing window.

Review Lesson 2-1: Classify each relation.

Vocabulary Review: Identify the constant in the expression.

Vocabulary Review: Identify the expressions that do not contain a constant term. Select all that apply.

Use Your Vocabulary: Identify the translation, reflection, stretch, and compression of the word Algebra.

Key Concept: Identify the function(s) that are NOT Power Functions.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success

Problem 4 Got It? Wind-Generated Power: The power P (in kilowatts) generated by a wind turbine varies directly as the cube of the wind speed v (in meters per second). A wind turbine generates 210 kW of power in a 12 mi/h wind. How much does this turbine generate in a 20 mi/h wind?

Error Analysis: Your friend says that he has found a way to transform the graph of the function below to obtain three real roots. Using the graph of the function, explain why this is impossible.
You may use the embedded Desmos utility below to graph the function.

Compare and Contrast: How are the graphs of the two functions below alike? different? What transformation was used to get the second equation?
You may use the embedded Desmos utility above to graph the functions.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

For a refresher on the Cornell note-taking system, click here.

Error Analysis: Your friend says that he has found a way to transform the graph of the function below to obtain three real roots. Using the graph of the function, explain why this is impossible.
You may use the embedded Desmos utility below to graph the function.

Compare and Contrast: How are the graphs of the two functions below alike? different? What transformation was used to get the second equation?
You may use the embedded Desmos utility above to graph the functions.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

For a refresher on the Cornell note-taking system, click here.