Answer:
a) 18
b)x^2+10x+18
c)x^2 -6x+2
Explanation:
This is a case of plugging in the value into f(x).
a) f(-8)= -8^2 + 6(-8) +2
f(-8)= 64 + (-48) +2
f(-8)=64 + (-46)
f(-8)=18
b) f(x+2)= (x+2)^2+6(x+2)+2
So here I'll take a break to explain what's going on, because x+2 is a binomial meaning two terms and it is being squared I have to multiply the whole thing by itself. Meaning: (x+2) x (x+2), this is also known as foiling!! and for the next part its distributing 6 into x and 2.
f(x+2)= x^2+4x+4+6x+12+2
I'll reorder it
f(x+2)= x^2+4x+6x+12+2+4
f(x+2)= x^2+10x+18
c) f(-x)= -x^2+6(-x) +2
f(-x)= x^2 -6x+2