Explanation:
since the x differences are constantly 1, we can focus only on the pure y differences point by point :
28 - 18 = 10
35 - 28 = 7
39 - 35 = 4
40 - 39 = 1
38 - 40 = -2
and now the second differences = the difference differences :
7 - 10 = -3
4 - 7 = -3
1 - 4 = -3
-2 - 1 = -3
because the second differences are constant, we have a quadratic relation.