a simple way to get the coordinates of the vertex, is, the constant outside the bars is the y-coordinate of the vertex, and to get the x-coordinate, we can simply find what values of x makes the barred expression to 0, and we can do that by simply zeroing out the barred expression and solving for x.
[tex]\bf f(x)=|3x-4|\implies f(x)=|3x-4|+\stackrel{\stackrel{y-coordinate}{\downarrow }}{0}
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\stackrel{\textit{to get the x-coordinate}}{3x-4=0}\implies 3x=4\implies x=\cfrac{4}{3}
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\rule{34em}{0.25pt}\\\\
~\hfill \stackrel{vertex}{\left( \frac{4}{3},0 \right)}~\hfill[/tex]
