Start by using -b/2a to find the x value of the vertex (which is where the minimum value would be).
-2/1 = -2 = x value of the vertex
Plug in the x value of the vertex to get the minimum value
1/2(-2)^2 + 2(-2) + 8
2 - 4 + 8
6 = y value of the vertex, which is also the minimum.
Therefore, the minimum value of the function is D. 6