Based on the definition of "big-O" notation, we have
6n
2
+18 ≤ cn
2
. Note that as long as
c>6
, we can always find out
N
such that
6n
2
+18 ≤ cn
2
when
n ≥ N
. Now choose
c=7
, then we can choose
N=5
since
6n
2
+18 ≤ 7n
2
6 + 18/n
2
≤ 7
18/n
2
≤ 1
n ≥ 5