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