### Home > A2C > Chapter 4 > Lesson 4.1.1 > Problem 4-5

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). Homework Help ✎*y*= (*x*− 2)^{2}*y*=*x*^{2}+ 2*y*= (*x*+ 3)^{2}*y*= −*x*^{2}+ 5Where on the graphs of each of the above equations would you find the points with the smallest or largest

*y*-values?

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

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?

When *x* is equal to 2, *y* is equal to 0, which is the smallest possible output.

Does this parabola open upward or downward?

It opens upward. Therefore, there will be a smallest output.

Lowest point: *x* = 0, *y* = 2

See part (a).

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