### Home > INT2 > Chapter 9 > Lesson 9.1.1 > Problem9-5

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)?

1. $f(x)=(x-1)^2$

Are there any $x$-values that yield a negative number?

It is impossible for the output to be negative in this case. What is the lowest value $f(x)$ can be? Can $f(x) = 0$?

$x = 1$

1. $f(x)=x^2-2$

Does this parabola open upward or downward?

It opens upward. Therefore, there will be a smallest output. What input yields the smallest output?

$x = 0$

1. $f(x) = (x + 2)^2$

See part (a).

1. $f(x) = -x^2 + 3$

See part (b). Notice the negative sign in front of the $x^2$ term. How does that change the parabola?

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