CPM Homework Help : CCA2 Problem 2-5

For each equation in parts (a) through (d) below, find the input value that gives the smallest possible output. In other words, find the $x$ -value of the lowest point on the graph. Then find 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. What is the lowest value $y$ can be? Can $y$ equal $0$ ?
Answer (a):
$x=2$

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

$y=(x+3)^2$
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?

Where on the graphs of each of the above equations would you find the points with the smallest or largest $y$ -values?