The vertex of the graph \(f(x)=4|x+6|\) is the point at which the function changes from decreasing to increasing.
Note that
- for all \(x<-6\) the function is decreasing;
- for all \(x>-6\) the function is increasing;
- at \(x=-6\) the function has zero and this point is the point at which the function changes from decreasing to increasing.
Since at \(x=-6\) the function has zero, then \(f(-6)=0.\) This means that vertex has coordinates (-6,0).
Answer: (-6,0)
