is the vertex of the graph y=(x+2)2 a max or min point

Question

y=(x+2)2    determine if the vertex of the graph is a maximum or minimum point

Answer 1

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.