1. The problem statement, all variables and given/known data Determine values of a, b, c in the formula ax^2+bx^2 +c that satisfy the conditions: f(0)=0 // Limx->-1 F(x)=3 // limx->2 f(x)=6 3. The attempt at a solution 1. F(0)=0 therefore x=0 so f(0)=a(0)^2+b(0)+c so f(0)=c = 0 so c=0 2. Lim f(x) = 3, x->-1 so f(x)=ax^2+bx+c 3 = a(-1)^2+(-b) + 0 so a= 3+b or b= a-3 3. f(x)=6 x->2 6 = ax^2 + bx + c 6 = 4a + 2b sub in a. 6=4(3+b) +2b -6 = 6b b=-1 now do the same but sub in b. to solve for a 6=4a+2b 6=4a + 2(a-3) 6=4a + 2a -6 12=6a a=2 So therefore values are a=2, b=-1 and c=0 to satisfy those conditons. I beleive this is the correct way to go about it, but i just wanted some one to check for me if possible, and also i was curious is it because you are expressing a in terms of be and b in terms of a when taking the limit, and substituting that value into the next limit restriction 6=4a+2b that it makes it follow all of the previous conditions... (ie: c=0, b=a-3 a=3+b) I was just curious if some one could give me some more understanding if this is correct.