17.8k views
4 votes
Find the vertex of the function y = ∣x−|1/2|∣ + 6.(1/2, 6)(1/2, -6)(-1/2, 6)(-1/2, -6)

1 Answer

2 votes

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)

User Amiola
by
3.0k points