Question

If f(x) = 3(x-2)^2 + 7 and g(x) = (x + 4)^2-5, which of the following represents the simplified form of
(f - g)(x)?

Answer 1

All you have to do is subtract g(x) from f(x):

[3(x-2)^2+7]-[(x+4)^2-5]

[3(x^2-4x+4)+7]-[(x^2+8x+16)-5]

(3x^2-12x+12+7)-(x^2+8x+11)

(3x^2-12x+19)-(x^2+8x+11)

2x^2-12x+19-8x+11

2x^2-20x+30

So the simplified form of (f-g)(x) is 2x^2-20x+30