Let's prove with x=1. The value of y is the sum of coefficients, and it would be 5
Option A. x=1, y=1+4+2-2→y=5 Ok
Option B. x=1, y=-1+4+2-2→y=3 No
Option C. x=1→y=1+4+2-2→y=5 Ok
Option D. x=1→y=1-4-2-2→y=-7 No
Then we have to options A or C
Let´s prove another point, for example (-1,-1), when x=-1, y=-1
Option A. x=-1→y=(-1)^4+4(-1)^3+2(-1)^2-2(-1)
y=1+4(-1)+2(1)+2=1-4+2+2→y=1 No
Option C. x=-1→y=(-1)^3+4(-1)^2+2(-1)-2
y=-1+4(1)-2-2=-1+4-2-2→y=-1 Ok
Answer: Option C. y=x^3+4x^2+2x-2
