Algebra 2 5-8 Complete Lesson: Polynomial Models in the Real World

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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In Your Own Words: Restate the (n + 1) Point Principle in your own words.

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Problem 1 Got It?

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Problem 2 Got It?

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Problem 3 Got It? If four data points are given, which type of regression function guarantee ensure a perfect fit?

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Problem 4 Got It? Create a table in the embedded Desmos utility 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 appropraite viewing window that contains all data points and the regression line.

We have released a new and improved Graphing question type! Students will no longer be able to answer this question.

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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 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.

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Vocabulary: Explain which form of estimation, interpolation or extrapolation, is more reliable.

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Reasoning: Is it possible to create a cubic function that passes through (0, 0), (-1, 1), (-2, 2), and (-3, 9)? Explain.

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Writing: The R² value for a quartic model is 0.94561. The R² value for a cubic model of the same data is 0.99817. Which model seems to show a better fit? Explain.

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Review Lesson 5-7: Expand the binomial.

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Review Lesson 5-7: Expand the binomial.

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Review Lesson 1-6: Write the compound inequality as an absolute value inequality.

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Review Lesson 1-6: Write the compound inequality as an absolute value inequality.

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Review Lesson 1-4: Solve the formula for the variable s.

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Review Lesson 1-4: Solve the formula for the variable r.

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Review Lesson 4-1: Graph the functions on the same coordinate plane. Zoom and pan your graph to establish an appropraite viewing window. Consider the similarities and differences between the graphs.

We have released a new and improved Graphing question type! Students will no longer be able to answer this question.

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Vocabulary Review: Drag each item from the left column to its corresponding model in the right column.

numerical data
airplane
house

floor plan
equation
model airplane

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Use Your Vocabulary: The points (1, 3) and (2, 6) are collinear. Extrapolate the y-value of the point on the same line when x = 4.

Fill in the blank: The point (4, ?) is also on the line.

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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.

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Reflection: Math Success

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Algebra 2 5-8 Complete Lesson: Polynomial Models in the Real World

In Your Own Words: Restate the (n + 1) Point Principle in your own words.

Problem 1 Got It?

Problem 2 Got It?

Problem 3 Got It? If four data points are given, which type of regression function guarantee ensure a perfect fit?

Vocabulary: Explain which form of estimation, interpolation or extrapolation, is more reliable.

Reasoning: Is it possible to create a cubic function that passes through (0, 0), (-1, 1), (-2, 2), and (-3, 9)? Explain.

Writing: The R² value for a quartic model is 0.94561. The R² value for a cubic model of the same data is 0.99817. Which model seems to show a better fit? Explain.

Review Lesson 5-7: Expand the binomial.

Review Lesson 5-7: Expand the binomial.

Review Lesson 1-6: Write the compound inequality as an absolute value inequality.

Review Lesson 1-6: Write the compound inequality as an absolute value inequality.

Review Lesson 1-4: Solve the formula for the variable s.

Review Lesson 1-4: Solve the formula for the variable r.

Review Lesson 4-1: Graph the functions on the same coordinate plane. Zoom and pan your graph to establish an appropraite viewing window. Consider the similarities and differences between the graphs.

Vocabulary Review: Drag each item from the left column to its corresponding model in the right column.

Use Your Vocabulary: The points (1, 3) and (2, 6) are collinear. Extrapolate the y-value of the point on the same line when x = 4.Fill in the blank: The point (4, __?__) is also on the line.

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! 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.

In Your Own Words: Restate the (n + 1) Point Principle in your own words.

Problem 1 Got It?

Problem 2 Got It?

Problem 3 Got It? If four data points are given, which type of regression function guarantee ensure a perfect fit?

Vocabulary: Explain which form of estimation, interpolation or extrapolation, is more reliable.

Reasoning: Is it possible to create a cubic function that passes through (0, 0), (-1, 1), (-2, 2), and (-3, 9)? Explain.

Writing: The R² value for a quartic model is 0.94561. The R² value for a cubic model of the same data is 0.99817. Which model seems to show a better fit? Explain.

Review Lesson 5-7: Expand the binomial.

Review Lesson 5-7: Expand the binomial.

Review Lesson 1-6: Write the compound inequality as an absolute value inequality.

Review Lesson 1-6: Write the compound inequality as an absolute value inequality.

Review Lesson 1-4: Solve the formula for the variable s.

Review Lesson 1-4: Solve the formula for the variable r.

Review Lesson 4-1: Graph the functions on the same coordinate plane. Zoom and pan your graph to establish an appropraite viewing window. Consider the similarities and differences between the graphs.

Vocabulary Review: Drag each item from the left column to its corresponding model in the right column.

Use Your Vocabulary: The points (1, 3) and (2, 6) are collinear. Extrapolate the y-value of the point on the same line when x = 4.Fill in the blank: The point (4, __?__) is also on the line.

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! 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.

Use Your Vocabulary: The points (1, 3) and (2, 6) are collinear. Extrapolate the y-value of the point on the same line when x = 4.

Fill in the blank: The point (4, ?) is also on the line.

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.

Use Your Vocabulary: The points (1, 3) and (2, 6) are collinear. Extrapolate the y-value of the point on the same line when x = 4.

Fill in the blank: The point (4, ?) is also on the line.

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.