Algebraic Geometry (2nd question)

[esisk]

Here is a similar one that again tells me that my undestanding of the notions is still not there. I would like to know why the the polynomials x^2, xy, y^2 generate the the structire sheaf on O_P1 (2).
Again I have attached the question. Thank you, any help is appreciated

 

[Hurkyl]

Isn't $\mathcal{O}_{\mathbb{P}^1}(2)$, by definition, the graded 2 part of the homogeneous coordinate ring?