To determine the vertex of the function [tex]\(h(x) = |x + 6| + 3\)[/tex], we need to understand the structure of absolute value functions. The general form of an absolute value function is:
[tex]\[ h(x) = |x - h| + k \][/tex]
where [tex]\((h, k)\)[/tex] represents the vertex of the function.
Given the function:
[tex]\[ h(x) = |x + 6| + 3 \][/tex]
we should aim to rewrite it in the general form [tex]\(|x - h| + k\)[/tex]. Notice that [tex]\(x + 6\)[/tex] can be written as [tex]\(x - (-6)\)[/tex]. Therefore, the function becomes:
[tex]\[ h(x) = |x - (-6)| + 3 \][/tex]
In this form, it is clear that [tex]\(h = -6\)[/tex] and [tex]\(k = 3\)[/tex]. Hence, the vertex of the function is:
[tex]\((h, k) = (-6, 3)\)[/tex]
So, the correct answer is:
B. [tex]\((-6, 3)\)[/tex]
