From the January 2016 Common Core Algebra I Regents

http://www.regentsprep.org/regents/math/algtrig/ate12/completesqlesson.htm

We can use the method of completing the square — see the link above
So far we have x^2 – 8x so we take 1/2 of -8 and square that to complete
(x –  4) (x – 4 ) giving x^2 – 8x + 16

trying answer (1) gives x^2 – 8x + 16 = 9  if we subtract 9 from each side we get:
x^2 – 8x + 7 = 0  close but no cigar

trying answer (2) gives x^2 – 8x + 16 = 23  if we subtract 23 from each side we get:
x^2 – 8x – 7 = 0  matches exactly!!!

OR

we can expand each answer and set it equal to zero to see which one matches the original whether on paper or on the TI-84
On the TI-84, set Y1 = x^2 – 8x – 7 and then set each answer choice to 0 and put into Y2 one by one
Try answer (1) by setting Y2 = (x – 4)^2 – 9, does it match Y1?
Try answer (2) by setting Y2 = (x – 4)^2 – 23, does it match Y1?  🙂