3n + 5n^2 + 1 | applying Big-O notation for the single terms
= O(3n) + O(5n^2) + O(1) | leaving out constant multipliers
= O(n) + O(n^2) + O(1) | taking the one with the maximum power
= O(n^2)
=> quadratic time
So you are right, the first option is the quadratic one.
If it was 3n + 5n^(2 + 1), then it would be qubical due to 5^(2 + 1) = 5^3.
solved Which equation represents quadratic time [closed]