Question

What is the vertex of `y=sqrt(x+2)`?

Answer 1

I do not think this function has a vertex (considered as the highes or lowest point as in a parabola).

Explanation:

The square root, such as this one, has a graph that looks like a horizontal half parabola.
If you mean the hypotetical vertex of the complete parabola then you have that its coordinates are `x=-2, y=0` but I am not sure it can be considered as a proper vertex:
The graph looks like this:
graph{sqrt(x+2) [-10, 10, -5, 5]}
As you can see you have only half parabola!