Polynomial Functions and Modeling

Polynomial Modeling

Polynomials of Best Fit

Technology can be used to generate a polynomial of best fit that approximates the closest relationship between two variables for a polynomial of a given degree.
Just as technology can be used to find a line or quadratic of best fit, it is possible to find other polynomials to fit a given set of data. Graphing calculators will commonly have regression functions up to degree 3 (cubic), but online tools can be used to fit polynomials of any degree.
Step-By-Step Example
Modeling Data Trends with Polynomial Functions

The table shows data values from an experiment. Identify the polynomial of best fit for the data.

xx yy
0.18 4.24
1.64 8.33
3.23 6.43
4.26 3.44
6.69 7.62
6.80 10.64
3.49 4.92
0.79 6.72
5.74 3.52
6.09 5.18
5.92 4.51
0.85 6.40
Step 1
Plot the data points.
Step 2

Look for a pattern.

The pattern displayed by the data points resembles a cubic polynomial.

Step 3

Use a graphing utility to identify the polynomial that best models the pattern of the data.

Follow the instructions for the graphing utility to identify the best fit curve. Use a polynomial curve of degree 3, based on the data plot.

Solution
The graphing utility will plot the curve and identify its algebraic rule.