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

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.

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.

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.