y=(x+2)2,
y'=2(x+2),
y"=2.
The second derivative is always positive so the vertex of this parabola (-2,0) is a minimum.
Another way to look at the values of y at and around x=-2:
x=-2, y=0: x<-2, y>0; x>-2, y>0. So on either side of x=-2 the graph is above y=0 (above the x-axis), making the vertex the minimum point.