The given function is:
[tex]y=|x-|\frac{1}{2}||+6[/tex]The vertex is given by the x-number that makes the argument inside the absolute value symbol equal to 0, so:
[tex]\begin{gathered} x-\frac{1}{2}=0 \\ \\ x=\frac{1}{2} \end{gathered}[/tex]Now, the y-coordinate of the vertex can be found by replacing x=1/2 and solving it as follows:
[tex]\begin{gathered} y=|\frac{1}{2}-|\frac{1}{2}||+6 \\ \\ y=|0|+6 \\ \\ y=6 \end{gathered}[/tex]The vertex is located at (1/2,6)
