6.2.5 Curve Fitting with Polynomial Models Key Objectives • Use finite differences to determine the degree of a polynomial that will fit a given set of data. • Use technology to find polynomial models for a given set of data. Example 1 Using Finite Differences to Determine Degree Finite differences can be used to determine the most appropriate type of function to model data, that is, the degree of the polynomial that best describes the data. If the difference in x -values is 1, the first differences are found by subtracting each y -value from the y -value that follows. The second differences are found by subtracting each first difference from the first difference that follows, and so on. If the first differences are constant, then the best model for the data is linear. If the second differences are constant, then the best model for the data is quadratic, and so on as shown in the table below.
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