# 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.

## Vocabulary

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, values will be different from those in the data set.

Remind students to check in general the differences in values 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.

### Image Attributions

## Description

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## Tags:

Activities
Answer Key
Answers
(45 more)
Assessment
CK.MAT.ENG.TE.1.Algebra-I.10
Common Misconceptions
completing the square
Concept Check and Troubleshooting
Differentiated Instruction
discriminant
double root
Enrichment
Inquiry Process
intercept form
line of symmetry
linear functions
linear regression
no real solutions
Pacing
parabolas
perfect squares
Problem Sets
Problem Solving
Pythagorean theorem
quadratic equation
quadratic equations
quadratic function
quadratic functions
quadratic regression
Quizzes
roots
scatter plot
Science Inquiry
Solution Key
Solutions
square roots
standard form
symmetric
Teacher Edition
Teaching Strategies
Teaching Strategies and Tips
Testing
Tests
vertex form
Worksheets
x-intercept
y-intercept
zeroes

## Subjects:

## Date Created:

Feb 22, 2012## Last Modified:

Aug 22, 2014
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