CPM Homework Help : INT3 Problem 2-50

For each equation, what input value will produce the smallest possible output? (In other words, what is the $x$ -value of the lowest point on the graph?) What is the input value that gives the largest possible output (or the $x$ -value of the highest point on the graph)?

$y=(x-2)^2$
Hint (a):
Are there any $x$ -values that yield a negative number?
More Help (a):
It is impossible for $y$ to be negative in this case. In turn, what is the lowest value $y$ can be? Can $y$ equal $0$ ?
Answer (a):
When $x$ is equal to $2$ , $y$ is equal to $0$ , which is the smallest possible output.

$y=x^2+2$
Hint (b):
Does this parabola open upward or downward?
More Help (b):
It opens upward. Therefore, there will be a smallest output.
Answer (b):
Lowest point: $x=0$ , $y=2$

$y=(x+3)^2$
Hint (c):
See part (a).

$y=-x^2+5$
Hint (d):
See part (b). Notice the negative sign in front of the $x^2$ term. How does that change the parabola?a