what is the function rule for this figure

Question

sides- 3 4 5 6 7
diagonals- 0 2 5 9 15

Answer 1

it describes the number of diagonals a polygon of n sides has
e.g for 4 sides, there are 2 diagonals
for 5 sides, there are 5 diagonals, et

the function rule is
diagonals(n) = C(n,2) - n
= n!/(2!(n-2)!) - n
= (n^2 - 3n)/2

BTW, for a 7-sided polygon there are 14 diagonals, not 15