### Question Description

for g(x)=x^2+2x+2, what is the function' s minimum or maximum value?

## Final Answer

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g(x) = x^2 + 2x +2 is a parabola with the "u" facing up.

g(0) = 0 + 0 + 2, Point at (0,2)

g(-2) = 4 -4 + 2 Point at (-2,2), So since the y values are the same when x= 0 and x= -2, Minimum would be at x=-1 (in the middle of 0 and -2)

g(-1) 1 - 2 + 2 Vertex (minimum) at (-1, 1)

Just to be sure, add a few other points:

g(1) = 1+ 2 + 2 Point at (1,5)

g(2) = 4 + 4 + 2 Point at (2, 8)

So the minimum value is at x=-1 and y=1

Since it is a parabola, it has no maximum value, (infinity). Parabolas typically go up the y scale as x gets bigger.