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2-50.

For each equation, what input value will produce 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. $y=(x-2)^2$

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

It is impossible for $y$ to be negative in this case. 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.

1. $y=x^2+2$

Does this parabola open upward or downward?

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

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

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?a