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y= 1/2(x-1)(x+2)
y=(1/2)(x^2+x-2)
complete the square:
y=(1/2)(x^2+x+1/4)-1-1/8
y=(1/2)(x+1/2)^2-9/8
This is an equation of a parabola that opens upwards.
Its standard form of equation:y=A(x-h)^2+k, (h,k)=(x,y) coordinates of the vertex
for given equation:y=(1/2)(x+1/2)^2-9/8
vertex: (-1/2,-9/8)
see graph below:
(