Question

Find the vertex of the absolute value function y = 1/2 |x – 2| - 1.(2, -1)(1/2, 2)(2, 1/2)(2, 1)

Answer 1

Solution:

Given the absolute value function below

$y=\frac{1}{2}\left|x-2\right|-1$

To find the vertex of the absolute value function, we will solve the absolute value function to find the absolute value zero(s) as shown below

$\begin{gathered} |x-2|=0 \\ x=2 \end{gathered}$

Where, x = 2, substitute 2 for x to find the value of y

$\begin{gathered} y=\frac{1}{2}|x-2|-1 \\ Where,\text{ }x=2 \\ y=\frac{1}{2}|2-2|-1=\frac{1}{2}|0|-1=0-1=-1 \\ y=-1 \end{gathered}$

Hence, the vertex absolute value function is

$\left(2,\:-1\right)$