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 absolute value vertex form

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

Step2: Rewrite the given function

Given \( h(x) = |x + 6| + 3 \), we can rewrite \( x + 6 \) as \( x - (-6) \). So the function becomes \( h(x) = |x - (-6)| + 3 \).

Step3: Identify h and k

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

Answer:

B. (-6,3)