To identify the vertex of the function [tex]\( f(x) = -|x - 3| - 4 \)[/tex], follow these steps:
1. Understand the general form of the function:
An absolute value function generally takes the form [tex]\( f(x) = a|bx - c| + d \)[/tex]. In this function [tex]\( f(x) = -|x - 3| - 4 \)[/tex], we can identify the following parameters:
- [tex]\( a = -1 \)[/tex]
- [tex]\( b = 1 \)[/tex]
- [tex]\( c = 3 \)[/tex]
- [tex]\( d = -4 \)[/tex]
2. Vertex of an absolute value function:
The vertex of an absolute value function [tex]\( a|bx - c| + d \)[/tex] is at [tex]\( (c, d) \)[/tex].
3. Substitute the values identified:
- Here, [tex]\( c = 3 \)[/tex] and [tex]\( d = -4 \)[/tex].
4. Vertex calculation:
Therefore, the vertex of the function [tex]\( f(x) = -|x - 3| - 4 \)[/tex] is at [tex]\( (3, -4) \)[/tex].
From the given choices:
- [tex]\((3, 4)\)[/tex]
- [tex]\((3, -4)\)[/tex]
- [tex]\((-3, 4)\)[/tex]
- [tex]\((-3, -4)\)[/tex]
The correct answer is [tex]\((3, -4)\)[/tex].
