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10.7: Linear, Exponential and Quadratic Models

Difficulty Level: At Grade Created by: CK-12

Learning Objectives

At the end of this lesson, students will be able to:

  • Identify functions using differences and ratios.
  • Write equations for functions.
  • Perform exponential and quadratic regressions with a graphing calculator.
  • Solve real-world problems by comparing function model.


Terms introduced in this lesson:

ratio of the differences
constant ratio of differences
exponential, quadratic regression

Teaching Strategies and Tips

Emphasize that students should always begin a regression by drawing the scatter plot of the data. This allows them to determine which function of best fit is most appropriate, if any.

Point out:

  • A regression is a curve that comes as close as possible to all the data points without being another type of function.
  • Regressions do not necessarily pass through data points. Therefore, yvalues will be different from those in the data set.

Remind students to check in general the differences in xvalues that they are constant.

Error Troubleshooting

In Review Questions 4-6 and 12, remind students to calculate the differences of the differences to see if a quadratic trend exists. Students often calculate only the first set of differences.

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