Ans is B
Another method apart from derivation
y= x^2 +x -2
lets make it a perfect square
y= x^2 +x +1/4 -1/4 -2
y = {(x+1/2)^2 -1/4} -2
y= (x+1/2)^2 -9/4
therefore we have y =z^2 -9/4
z can be minimum 0 when x=-1/2
so y will be minimum put z=0 so y=-9/4
Another method apart from derivation
y= x^2 +x -2
lets make it a perfect square
y= x^2 +x +1/4 -1/4 -2
y = {(x+1/2)^2 -1/4} -2
y= (x+1/2)^2 -9/4
therefore we have y =z^2 -9/4
z can be minimum 0 when x=-1/2
so y will be minimum put z=0 so y=-9/4
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