Answer:
The vertex is the point [tex](-\frac{1}{3},0)[/tex]
Step-by-step explanation:
we know that
The general form of an absolute value equation is
[tex]y=a\left|x-h\right|+k[/tex]
The variable a tells us how far the graph stretches vertically, and whether the graph opens up or down. The variables h, and k, tell us how far the graph shifts horizontally and vertically
The vertex is the point (h,k)
we have
[tex]f(x)=\left|3x+1\right|[/tex]
Rewrite the expression (3x+1)
[tex](3x+1)=\frac{3}{3} (3x+1)=3(x+\frac{1}{3})[/tex]
substitute
[tex]f(x)=\left|3(x+\frac{1}{3})\right|[/tex]
[tex]f(x)=3\left|(x+\frac{1}{3})\right|[/tex]
[tex]a=3\\h=-\frac{1}{3}\\k=0[/tex]
therefore
The vertex is the point [tex](-\frac{1}{3},0)[/tex]
see the attached figure to better understand the problem
