Question

select the correct answer.
which point is the vertex of the graph defined by ( f(x) = 6|x - 2| - 5 )?

a. ( (6, 5) )
b. ( (2, -5) )
c. ( (0, 0) )
d. ( (6, -2) )

Explanation:

Step1: Recall the vertex form of absolute value function

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

Step2: Identify \( h \) and \( k \) from the given function

For the function \( f(x) = 6|x - 2| - 5 \), we compare it with the general form. Here, \( h = 2 \) and \( k = -5 \).

Step3: Determine the vertex

Using the values of \( h \) and \( k \), the vertex of the graph is \((h, k)=(2, -5)\).

Answer:

B. \((2, -5)\)