Question

11
select the correct answer from each drop-down menu.
consider absolute value function f.
$f(x) = -\frac{2}{3} | x + 4 |$
the vertex of the function is a at .

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 the vertex is at \( (h, k) \). If \( a < 0 \), the parabola (graph of absolute value function) opens downward, so the vertex is a maximum point.

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

Given \( f(x) = -\frac{2}{3}|x + 4| \), we can rewrite it as \( f(x) = -\frac{2}{3}|x - (-4)| + 0 \). Comparing with \( f(x) = a|x - h| + k \), we have \( h = -4 \), \( k = 0 \), and \( a = -\frac{2}{3} \) (which is less than 0, so the vertex is a maximum).

Step3: Determine the vertex and its type

Since \( a = -\frac{2}{3}<0 \), the vertex \( (-4, 0) \) is a maximum point.

Answer:

The vertex of the function is a maximum at \( (-4, 0) \)