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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 ✎

1. $y=(x−2)^2$

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

It is impossible for $y$ to be negative in this case. What is the lowest value $y$ can be? Can $y$ equal $0$?

$x=2$

1. $y=x^2+2$

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

See part (a).

1. $y=−x^2+5$

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

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