Use finite differences to identify the degree of the polynom

Use finite differences to identify the degree of the polynomial that best describes the data. linear cubic quartic quadratic The table shows the numbers of ships that visited a port in the past 5 years. Identify a polynomial function for the number of ships in thousands that visited the port in a given year.

Solution

We can see from the finite differnecs that 2 differenc becomes constant

So, polynomial is a quadratic

x	y	1st y diff	2nd diff
-3	4
-1	6	2
1	1	-5	-7
3	-11	-12	-7
5	-30	-19	-7
7	-56	-26	-7