What is the maximum value of x^2- 8x + 12?

That is a parabola that opens upward. There is no maximum value, it goes on forever. I guess you could say infinity is the maximum but I'm reluctant to make the mistake of treating infinity as a number.

You are right. There is NO maximum.

The maximum value of - x^2 -8x+12 would occur at x = -b/2a = -4

use this value in the equation to calculate the max value

Similarly , the MINIMUM value of x ^2 -8x+12 would occur at x = -b/2a = 4 calculate the min value by sub'ing in x = 4