Question

What is the vertex of the graph of g(x)=|x-9|+3

Answer 1

Look at h(x) = |x-9|. The vertex of this absolute value function graph is at (9,0).

Sometimes it helps to work on a simpler problem first, which is why I've introduced h(x) = |x-9|.

The vertex of g(x)=|x-9|+3 is 0+3, or 3; we translate the entire graph of g(x)=|x-9| upward by 3 units. Thus, the vertex of g(x) is (9,3).