To determine the vertex of the graph of the function [tex]\( g(x) = |x - 8| + 6 \)[/tex], let's analyze the structure of this equation.
1. Understand the Absolute Value Function:
The basic form of an absolute value function is [tex]\( g(x) = |x - h| + k \)[/tex], where [tex]\((h, k)\)[/tex] represents the vertex of the function.
2. Identify [tex]\( h \)[/tex] and [tex]\( k \)[/tex]:
- In [tex]\( g(x) = |x - 8| + 6 \)[/tex], the expression inside the absolute value is [tex]\( x - 8 \)[/tex]. This indicates that the value [tex]\( h \)[/tex], which makes the expression zero, is [tex]\( 8 \)[/tex].
- The constant term added outside the absolute value is [tex]\( 6 \)[/tex], representing [tex]\( k \)[/tex].
3. Vertex Coordinates:
- The coordinates of the vertex for the function [tex]\( g(x) = |x - 8| + 6 \)[/tex] are given by [tex]\( (h, k) \)[/tex].
- Therefore, the vertex of the function is [tex]\( (8, 6) \)[/tex].
Given this analysis, the vertex of the graph of [tex]\( g(x) = |x - 8| + 6 \)[/tex] is [tex]\( (8, 6) \)[/tex].
So, the correct answer is:
[tex]\[
\boxed{(8, 6)}
\][/tex]
