I think my answer should be correct.

What's wrong?

Supposethat S: {axz+bx+c:a,b,ceR, a>0} is the set of quadratic functions which have graphs opening upwards. Dene addition of functions by the usual rule, so that for example (3x2 2.x+ 1)+(5x2 +4x+ 17) = 8x2 +2x+18, and define scalar multiplication also by the usual mle, so that for example 5(3x2 2.x +1) = 15x2 10x + 5. Which of the following 10 properties of a vector space are satised? 1.Closure under Addition. Iff, g e S, thenf + g e S, 2.Associative Law ofAddition. lff, g, h e S, then (f + g) + h =f + (g + h), 3. Commutative Law of Addition. lff, g e S, thenf + g = g +f. 4. Existence of Zero. There exists an element 0 e S such that, for all f e S , f + 0 = f _ 5. Existence of Negative. For each f e S there exist an element 11 e S (usually written as f ) such that f + h = 0_ 6. Closure under Multiplication by a Scalar. lff E S and 11 E R , then 1f 5 S_ 7.Associative Law of Multiplication by a Scalar. If it, p 6 IR and f e S then 1104f) = (3441f- a. Scalar Multiplication Identity. If f e S then If = f , 9. Scalar Distributive Law. lfA, p 6 IR andf e S, then (/1 +p1f = if +pf. 10. Vector Distributive Law. lfjt 6 IR and f , g E S, then 3,0\" + g) = if + 113;. Enter your answer as a subset of {1 ,2,3,...,10}. (2.3.4.5,8no} 6