Question

what is the vertex of the graph of $g(x)=|x - 8|+6$?\
$\bigcirc\\ (6, 8)$\
$\bigcirc\\ (8, 6)$\
$\bigcirc\\ (6, -8)$\
$\bigcirc\\ (-8, 6)$

Explanation:

Step1: Recall the vertex form of absolute value function

The general form of an absolute value function is \( y = |x - h| + k \), where \((h, k)\) is the vertex of the graph.

Step2: Identify h and k from the given function

For the function \( g(x) = |x - 8| + 6 \), comparing it with \( y = |x - h| + k \), we have \( h = 8 \) and \( k = 6 \).

Step3: Determine the vertex

So the vertex of the graph of \( g(x) \) is \((h, k)=(8, 6)\).

Answer:

(8, 6)