What is the vertex of the absolute value function defined by ƒ(x) = |x + 2| + 4?

That "|x + 2|" indicates that the vertex of the most basic absolute value function, y=|x|, has been shifted 2 units to the left.  That "+4" indicates that the vertex has been shifted 4 units up.  Thus, the vertex of f(x)=|x+2|+4 is (-2,4).