smc

A simple method of solving the problem is trying each of the answer choices. One can plug in values of x and y for each, because many x-values and their single corresponding y-values are given. 1. Choice A works for (1,3) and (2,7) but fails to work on (3,13) because 3*4=12 and 12-1=11, not 13. 2. Choice B doesn't work for (2,7) because it would be 8-4+2+2=8, not 7. 3. Choice C actually works for all five pairs, being 1+1+1=3, 4+2+1=7, 9+3+1=13, 16+4+1=21, and 25+5+1=31. Thus, the answer is $\boxed{y=x^2+x+1}$.