Express f(x) in the form A(x+B)^2 + C, where A, B and C are constants to be determined.
I just don't get this at all, we haven't done it in class so I don't know why it's been set as a homework question, yes one of many..woohoo!! Any help greatly appreciated.
Just expand A(x+B)^2 + C, giving A.x^2 + A.2Bx + A.B^2 + C and equate this to 2x^2+8x+2. Looking at the x^2 term we have A = 2. Looking at the x term we have 2AB = 8. Looking at the constant term we have AB^2+C = 2. Taking the equations in this order gives you the values of A, then B, then C.
Have you reached completing the squares?
f(x) = 2x^2 +8x +2
f(x) = [2x^2 +8x] +2
f(x) = 2[x^2 +4x] +2
f(x) = 2[x^2 +4x +(4/2)^2 -(4/2)^2] +2
f(x) = 2[(x+2)^2 -4] +2
f(x) = 2[(x+2)^2] +2(-4) +2
f(x) = 2(x+2)^2 -8 +2
f(x) = 2(x+2)^2 -6 ----------answer.