Algebra 2 5-8 Guided Practice: Polynomial Models in the Real World

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Video Check: Select all that apply with regards to the video embedded directly above this item.

You are designing a patio. Square A is where you will place your grill. You are experimenting with your design by varying the size of square B. 

The table shows the total patio area for each of five different lengths x.

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Video Check: Select all that apply with regards to the video embedded directly above this item.

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Take Note: Restate The (n + 1) Point Principle in your own words.

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Take Note: Match each Desmos regression notation with the appropriate model.

Draggable item		Corresponding Item

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Problem 1 Got It?

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Video Check: Select all that apply with regards to the video embedded directly above this item.

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Take Note: Summarize the process of modeling data that is used in Problem 2.

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Problem 2 Got It?

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Video Check: Select all that apply with regards to the video embedded directly above this item.

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Problem 3 Got It? If four data points are given, which type of regression function can guarantee a perfect fit?
HINT: Recall The (n+1) Point Principle.

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Video Check: Select all that apply with regards to the video embedded directly above this item.

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Take Note: Define interpolation. You may use the canvas to help illustrate your written definition.

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Take Note: Define extrapolation. You may use the canvas to help illustrate your written definition.

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Take Note: Consider modeling the data in the table.
Classify each year in the left column below based on whether estimating cheese consumption that year is an example of interpolation or extrapolation.

2000
1890
1995
2050
1950
2019
2005

Interpolation
Extrapolation

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Problem 4 Got It?
Create a table at desmos.com and use it to find a linear regression model of the cheese consumption data. Let x = years since 1900. Recall Desmos' linear regression notation: y1~ax1+b.
Zoom and pan your graph to establish an appropriate viewing window that contains all data points and the regression line.
Take a screenshot of your graph and upload or paste it to the Formative canvas.

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Problem 4 Got It? Use the model you created above to estimate cheese consumption for 1980, 2000, and 2012 algebraically and/or graphically. Remember that you were instructed to let x represent years since 1900.
Also, identify the prediction years in which you can have the most and least confidence.
Hint: Consider interpolation vs extrapolation.

26.31 lb
23.07 lb
21.53 lb
17.7 lb
1980
2000
2012

Estimated consumption in 1980
Estimated consumption in 2000
Estimated consumption in 2012
Two prediction years with greatest confidence
Prediction year with least confidence

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Algebra 2 5-8 Guided Practice: Polynomial Models in the Real World

Video Check: Select all that apply with regards to the video embedded directly above this item.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Restate The (n + 1) Point Principle in your own words.

Take Note: Match each Desmos regression notation with the appropriate model.

Problem 1 Got It?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Summarize the process of modeling data that is used in Problem 2.

Problem 2 Got It?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Problem 3 Got It? If four data points are given, which type of regression function can guarantee a perfect fit?
HINT: Recall The (n+1) Point Principle.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Define interpolation. You may use the canvas to help illustrate your written definition.

Take Note: Define extrapolation. You may use the canvas to help illustrate your written definition.

Take Note: Consider modeling the data in the table.
Classify each year in the left column below based on whether estimating cheese consumption that year is an example of interpolation or extrapolation.

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Solve It! Based on the pattern in the table, find the total area when x is 5.

Solve It! What type of polynomial function does the data fit? Explain.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Restate The (n + 1) Point Principle in your own words.

Take Note: Match each Desmos regression notation with the appropriate model.

Problem 1 Got It?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Summarize the process of modeling data that is used in Problem 2.

Problem 2 Got It?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Problem 3 Got It? If four data points are given, which type of regression function can guarantee a perfect fit?
HINT: Recall The (n+1) Point Principle.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Define interpolation. You may use the canvas to help illustrate your written definition.

Take Note: Define extrapolation. You may use the canvas to help illustrate your written definition.

Take Note: Consider modeling the data in the table.
Classify each year in the left column below based on whether estimating cheese consumption that year is an example of interpolation or extrapolation.

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Solve It! Based on the pattern in the table, find the total area when x is 5.

Solve It! What type of polynomial function does the data fit? Explain.

Algebra 2 5-8 Guided Practice: Polynomial Models in the Real World

Algebra 2 5-8 Guided Practice: Polynomial Models in the Real World

Video Check: Select all that apply with regards to the video embedded directly above this item.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Restate The (n + 1) Point Principle in your own words.

Take Note: Match each Desmos regression notation with the appropriate model.

Problem 1 Got It?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Summarize the process of modeling data that is used in Problem 2.

Problem 2 Got It?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Problem 3 Got It? If four data points are given, which type of regression function can guarantee a perfect fit?HINT: Recall The (n+1) Point Principle.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Define interpolation. You may use the canvas to help illustrate your written definition.

Take Note: Define extrapolation. You may use the canvas to help illustrate your written definition.

Take Note: Consider modeling the data in the table. Classify each year in the left column below based on whether estimating cheese consumption that year is an example of interpolation or extrapolation.

🧠 Retrieval Practice:Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Solve It! Based on the pattern in the table, find the total area when x is 5.

Solve It! What type of polynomial function does the data fit? Explain.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Restate The (n + 1) Point Principle in your own words.

Take Note: Match each Desmos regression notation with the appropriate model.

Problem 1 Got It?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Summarize the process of modeling data that is used in Problem 2.

Problem 2 Got It?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Problem 3 Got It? If four data points are given, which type of regression function can guarantee a perfect fit?HINT: Recall The (n+1) Point Principle.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Define interpolation. You may use the canvas to help illustrate your written definition.

Take Note: Define extrapolation. You may use the canvas to help illustrate your written definition.

Take Note: Consider modeling the data in the table. Classify each year in the left column below based on whether estimating cheese consumption that year is an example of interpolation or extrapolation.

🧠 Retrieval Practice:Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Solve It! Based on the pattern in the table, find the total area when x is 5.

Solve It! What type of polynomial function does the data fit? Explain.

Problem 3 Got It? If four data points are given, which type of regression function can guarantee a perfect fit?
HINT: Recall The (n+1) Point Principle.

Take Note: Consider modeling the data in the table.
Classify each year in the left column below based on whether estimating cheese consumption that year is an example of interpolation or extrapolation.

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Problem 3 Got It? If four data points are given, which type of regression function can guarantee a perfect fit?
HINT: Recall The (n+1) Point Principle.

Take Note: Consider modeling the data in the table.
Classify each year in the left column below based on whether estimating cheese consumption that year is an example of interpolation or extrapolation.

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?