Question

select the correct answer. what is the vertex of the function ( f(x) = -\frac{1}{4}|x + 8| - 6 )? options: (-8, -6), (-8, 6), (8, -6), (8, 6)

Explanation:

Step1: Recall vertex form of absolute function

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

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

The given function is \(f(x)=-\frac{1}{4}|x + 8|-6\). We can rewrite \(x + 8\) as \(x-(-8)\). Comparing with the general form \(y=a|x - h|+k\), we have \(h=-8\) and \(k = - 6\). So the vertex of the function \(f(x)=-\frac{1}{4}|x + 8|-6\) is \((-8,-6)\). Wait, looking at the options, maybe there is a typo in the function. If the function is \(f(x)=-\frac{1}{4}|x - 8|-6\), then \(h = 8\) and \(k=-6\), but the options have \((-8, - 6)\) as one of the options (the first option: \((-8,-6)\)). Let's re - check the general form. The standard form is \(y=a|x - h|+k\), so for \(y =-\frac{1}{4}|x+8|-6=-\frac{1}{4}|x-(-8)|+(-6)\), so \(h=-8\) and \(k = - 6\). So the vertex is \((-8,-6)\).

Answer:

\((-8,-6)\) (assuming the first option is \((-8,-6)\))