Answer:
The vertex is at
[tex](2,-7)[/tex]
Step-by-step explanation:
We can get the vertx by graphing or by analysing the function.
Let's analyse.
The parent function of the given one is
[tex]g(x)=|x|[/tex]
And the given one is [tex]f(x)=|x-2|-7[/tex]
Specifically, the given function is a transformed function moved 2 units rightwards and 7 downwards.
We know that the parent function has vertex at [tex](0,0)[/tex], but with these decribed transformation, the function has vertex at [tex](2,-7)[/tex].
You can see this in the image attached, which shows the given function and its vertex.
Therefore, the vertex is at [tex](2,-7)[/tex]
