Question

Find the vertex of the function y = ∣x−|1/2|∣ + 6.(1/2, 6)(1/2, -6)(-1/2, 6)(-1/2, -6)

Answer 1

The given function is:

`y=|x-|(1)/(2)||+6`

The vertex is given by the x-number that makes the argument inside the absolute value symbol equal to 0, so:

`\begin{gathered} x-(1)/(2)=0 \\ \\ x=(1)/(2) \end{gathered}`

Now, the y-coordinate of the vertex can be found by replacing x=1/2 and solving it as follows:

`\begin{gathered} y=|(1)/(2)-|(1)/(2)||+6 \\ \\ y=|0|+6 \\ \\ y=6 \end{gathered}`

The vertex is located at (1/2,6)