what point is the vertex for the graph of y = |x| + 2?

The vertex of [tex]y=|x|[/tex] is [tex](0,0)[/tex]. The vertex of [tex]y=|x|+2[/tex] is the vertex of [tex]y=|x|[/tex] moved 2 units up. So its [tex](0,0+2)=\boxed{(0,2)}[/tex]