CPM Homework Help : INT2 Problem 8-108

Does each expression below have a maximum or a minimum possible value? What real-number value of $x$ will yield the maximum or minimum value? Where do you see these values in each expression?

Hint:

Each of these expressions has a squared quantity. What is the lowest number you can get when squaring?

$(x + 4)^2$
Answer (a):
Minimum:
$x = -4$

$-(x + 27)^2$
Answer (b):
If you try various values for $x$ you will almost always get a negative number. Therefore $0$ is the highest number you can obtain.
Maximum: $x = -27$

$-(x - 40)^2$

$(x + 32)^2$