Answer:
The vertex is at
\((2,-7)\)
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
\(g(x)=|x|\)
And the given one is \(f(x)=|x-2|-7\)
Specifically, the given function is a transformed function moved 2 units rightwards and 7 downwards.
We know that the parent function has vertex at \((0,0)\), but with these decribed transformation, the function has vertex at \((2,-7)\).
You can see this in the image attached, which shows the given function and its vertex.
Therefore, the vertex is at \((2,-7)\)
