# 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.

$x$ $y$
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.