5-8 Polynomial Models in the Real World

Objective

To fit data to linear, quadratic, cubic, or quartic models

A solve it problem with Anya.
Image Long Description

Polynomial functions can be degree 0 (constant), degree 1 (linear), degree 2 (quadratic), degree 3 (cubic), and so on.

Essential Understanding You can use polynomial functions to model many real-world situations. The behavior of the graphs of polynomial functions of different degrees can suggest what type of polynomial will best fit a particular data set.

You can use a graphing calculator to help you find functions that model the data in the table shown here.

x y
0 10.1
5 2.8
10 8.1
15 16.0
20 17.8

Enter the data into calculator lists L1 and L2. Use three different regressions: LINREG, QUADREG, and CUBICREG.

Graph each regression function and the scatter plot of the data in the same window. For this data, the cubic function appears to be a perfect fit.

Three graphing calculator screens.
Image Long Description


End ofPage 331

Table of Contents

Prentice Hall Algebra 2 Chapter 1 Expressions, Equations, and Inequalities Chapter 2 Functions, Equations, and Graphs Chapter 3 Linear Systems Chapter 4 Quadratic Functions and Equations Chapter 5 Polynomials and Polynomial Functions Chapter 6 Radical Functions and Rational Exponents Chapter 7 Exponential and Logarithmic Functions Chapter 8 Rational Functions Chapter 9 Sequences and Series Chapter 10 Quadratic Relations and Conic Sections Chapter 11 Probability and Statistics Chapter 12 Matrices Chapter 13 Periodic Functions and Trigonometry Chapter 14 Trigonometric Identities and Equations Skills Handbook English/Spanish Illustrated Glossary Selected Answers Index Acknowledgments