A sequence is quadratic if its terms have the explicit form an = An2 + Bn + C. The first three terms of the given sequence are a1 = 11, a2 = 14, and a3 = 19. Substituting these into the explicit form gives a system of three equations in three variables:
11 = A + B + C
14 = 4A + 2B + C
19 = 9A + 3B + C
Solve this system to get A = 1, B = 0, C = 10, which means that an = n2 + 10.