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Since this function is a parabola, the minimum value will be at the vertex
The x value of the vertex is found using -b/2a
= -2/2 = -1
Now we plug that into the function
g(-1) = -1^2 + 2(-1) + 2 = 1 - 2 + 2 = 1
Therefore, the function's minimum is 1
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