Clue #2: Notice how the closest integer values go 1,3,5,7. Also realize that, f(0) will give you the constant term (the last term in the quadratic).
Please try to do this yourself before you look at the answer. I assure you will feel much more satisfied and will have gained and learned more.
So, if you're still stuck, or want to check your answer, this is the answer I got which I'm quite sure is right: