Answer:
f(x)= -(x-2)^2+2
Explanation:
the same valuve needs the be added to both sides
f(x)+?= -x^2+4x+?-2
to complete the square -x^2+4x-4= -(x-2)^2 add the -4 to the expression
f(x)+?= -x^2+4x-4-2
since -4 was added to the right side, also add -4 the the left side
f(x)-4= -x^2+4x+?-2
now factor out the negative sign from the expression
f(x)-4= -(x^2-4x+4)-2
using a^2-ab+b^2=(a-b)^2
f(x)-4= -(x-2)^2-2
move the constant the the right side and change its sign
f(x)= -(x-2)^2-2+4
now calculate the sum
f(x)= -(x-2)^2+2