CPM Homework Help : INT2 Problem 9-5

For each equation in parts (a) through (d) below, determine the input value that gives 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)?

$f(x)=(x-1)^2$
Hint (a):
Are there any $x$ -values that yield a negative number?
More Help (a):
It is impossible for the output to be negative in this case. What is the lowest value $f(x)$ can be? Can $f(x) = 0$ ?
Answer (a):
$x = 1$

$f(x)=x^2-2$
Hint 1(b):
Does this parabola open upward or downward?
Hint 2(b):
It opens upward. Therefore, there will be a smallest output. What input yields the smallest output?
Answer (b):
$x = 0$

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

$f(x) = -x^2 + 3$
Hint (d):
See part (b). Notice the negative sign in front of the $x^2$ term. How does that change the parabola?

For each function above, where on its graph is the maximum or minimum point?