Rewrite as the opposite of the square of a binomial: −x^2+8x−16

Answer 1

opposite of a square? Must be a square root. (probably not a circle)

subtraction is the opposite or the reverse or inverse of addition

square roots are the opposite or the inverse of squares

f(x) = x^2 has an inverse relation f^-1(x) = sqr(x)

replace x with y in y = -x^2 + 8x - 16 and solve for the new y

y = 4- x^2/64

4-x^2/64 is the inverse relation

or

-x^2 + 8x -16

= -(x^2 -8x +16)

= - (x-4)^2

= (i)^2(x-4)^2

= [i(x-4)]^2

i(x-4) is the square root of -x^2+8x-16

[i(x-4)]^2 = -x^2 + 8x -16