Question

select the correct answer.
what is the vertex of the function $h(x) = |x + 6| + 3?$
a. $(-6,-3)$
b. $(-6,3)$
c. $(6,3)$
d. $(6,-3)$

Explanation:

Step1: Recall the vertex form of an absolute value function

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

Step2: Rewrite the given function in the general form

The given function is \( h(x) = |x + 6| + 3 \). We can rewrite \( x + 6 \) as \( x - (-6) \), so the function becomes \( h(x) = |x - (-6)| + 3 \).

Step3: Identify the vertex

Comparing with the general form \( y = |x - h| + k \), we have \( h = -6 \) and \( k = 3 \). So the vertex is \((-6, 3)\).

Answer:

B. (-6,3)