Question

What is the vertex of this function. (Possibly explain why so I understand the problem)

Answer 1

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.

$\bf f(x)=|3x-4|\implies f(x)=|3x-4|+\stackrel{\stackrel{y-coordinate}{\downarrow }}{0} \\\\\\ \stackrel{\textit{to get the x-coordinate}}{3x-4=0}\implies 3x=4\implies x=\cfrac{4}{3} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{vertex}{\left( \frac{4}{3},0 \right)}~\hfill$