Order at most and order at least

Hello,
I have to prove that 1/4n(n+1)-1/2 is order exactly n^2
I thought that it would be bounded order at most for big n^2 for all n>=1 but in this case how could it have an order at least. Is my order at most wrong? Thank you

Do you have an image of the question?

This is all my teacher gave me

Not sure what the E(n) means and I'm presuming the O(n^2) is the big O notation.
In this context, it really just means that C(n) is a quadratic. For large n, when n doubles then C(n) will quadruple.
Simply expand C(n) into the usual n^2, n, constant terms and make the argument that the quadratic is dominant term.

Sorry, I think they're both meant I be C(n). And the big symbol means both big o and omega so I need to shown that it can be less then or equal depending on the coefficient on n^2

In the image is it
Theta(n^2)
or
O(n^2)

Theta

Ok, so you need to show that there is both a
* quadratic upper bound: c*n^2 for n>n0
and a
* quadratic lower bound: d*n^2 for n>n0
Have a go at doing either / both and if you have problems just post? Some examples at
http://www-cgrl.cs.mcgill.ca/~godfried/teaching/dm-reading-assignments/Growth-of-Functions.pdf