We can use finite differences and a scatter plot to help us decide the appropriate polynomial model for a given data set.
See solution.
Practice makes perfect
One way to determine if a data set fits a polynomial of specific degree is by calculating the differences of the y-values corresponding to equally-spaced x-values. These are called finite differences. Let's review the properties of finite differences.
If the nth differences of equally-spaced data are nonzero and constant, then the data can be represented by a polynomial of degree n.
According to the property of finite differences mentioned above, if the third differences are constant, then we can know that a data set fits a cubic function. An example for a situation like this is shown below.
An alternative way is by drawing a scatter plot. Then we can see the behavior of the data set and decide if it suggests using a cubic model. If that is the case, we can use the regression feature of a graphic calculator to find the cubic function of best fit.
