Question

what is the vertex of the function $h(x) = -4|x - 6| + 2$?
$(2, -6)$
$(2, 6)$
$(6, 2)$
$(-6, 2)$

Explanation:

Step1: Recall the vertex form of absolute value function

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

Step2: Identify h and k from the given function

For the function \( h(x) = -4|x - 6| + 2 \), we can see that \( h = 6 \) and \( k = 2 \).

Step3: Determine the vertex

Using the vertex form, the vertex is \( (h, k)=(6, 2) \).

Answer:

(6, 2)