Well, what do you know? You are clearly expected here to know what a "basis" is- it must span the space and be independent. Any "vector" in , the space of polynomials, with real coefficients, of degree 2 or less, is of the form . To show that these functions, 1, x+ r, and span the space you must show that whatever a, b, and c are, there exist numbers, , , and [tex]\gamma[/b] such that . To show that they are independent, you must show that the only way you can have , for all x, is to have .