When more than three data points suggest a quadratic function, you can use the quadratic regression feature of a graphing calculator to find a quadratic model.
Problem 3 Using Quadratic Regression
The table shows a meteorologist's predicted temperatures for an October day in Sacramento, California.
| Time | Predicted Temperature (°F) |
|---|---|
| 8 A.M. | 52 |
| 10 A.M. | 64 |
| 12 P.M. | 72 |
| 2 P.M. | 78 |
| 4 P.M. | 81 |
| 6 P.M. | 76 |
Think
How do you write times using a 24-hour clock?
Add 12 to the number of hours past noon. So, 2 P.M. is 14:00 in the 24-hour clock.
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What is a quadratic model for this data?
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Step 1 Enter the data. Use the 24-hour clock to represent times after noon.
Image Long Description -
Step 2 Use QuadReg.
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Step 3 Graph the data and the function.
A quadratic model for temperature is
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Use your model to predict the high temperature for the day. At what time does the high temperature occur?
Use the Maximum feature or tables.
Predict the high temperature for the day to be 79.4°F at about 3:42 P.M.
✓ Got It?
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The table shows a meteorologist's predicted temperatures for a summer day in Denver, Colorado. What is a quadratic model for this data? Predict the high temperature for the day. At what time does the high temperature occur?
Denver, CO Time Predicted Temperature (°F) 6 A.M. 63 9 A.M. 76 12 P.M. 86 3 P.M. 89 6 P.M. 85 9 P.M. 76
Table of Contents
- 5-1 Polynomial Functions
- 5-2 Polynomials, Linear Factors, and Zeros
- 5-3 Solving Polynomial Equations
- 5-4 Dividing Polynomials
- 5-5 Theorems About Roots of Polynomial Equations
- 5-6 The Fundamental Theorem of Algebra
- 5-7 The Binomial Theorem
- 5-8 Polynomial Models in the Real World
- 5-9 Transforming Polynomial Functions