Select the correct answer.

What is the vertex of the function [tex]f(x)=-\frac{1}{2}|x+8|-5[/tex]?

A. [tex](-8,-5)[/tex]
B. [tex](-8,5)[/tex]
C. [tex](8,5)[/tex]
D. [tex](8,-5)[/tex]



Answer :

To determine the vertex of the function [tex]\( f(x) = -\frac{1}{2}|x+8| - 5 \)[/tex], we need to express the function in its vertex form. The vertex form of an absolute value function is given by:
[tex]\[ f(x) = a|x - h| + k \][/tex]
where [tex]\((h, k)\)[/tex] is the vertex of the function, and [tex]\(a\)[/tex] determines the vertical stretch/compression and the direction of the opening.

The given function is:
[tex]\[ f(x) = -\frac{1}{2} |x + 8| - 5 \][/tex]

We can rewrite this function to match the vertex form:
[tex]\[ f(x) = -\frac{1}{2} |x - (-8)| + (-5) \][/tex]

From this form, we identify the parameters [tex]\(h\)[/tex] and [tex]\(k\)[/tex]:
[tex]\[ h = -8 \][/tex]
[tex]\[ k = -5 \][/tex]

Thus, the vertex of the function is [tex]\((-8, -5)\)[/tex].

So, the correct answer is:
A. [tex]\((-8, -5)\)[/tex]