Answered

Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

Identify the vertex of the following function:

[tex]\[ f(x) = -|x-3| - 4 \][/tex]

A. [tex]\((3, 4)\)[/tex]

B. [tex]\((3, -4)\)[/tex]

C. [tex]\((-3, 4)\)[/tex]

D. [tex]\((-3, -4)\)[/tex]

Sagot :

GinnyAnswer
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].
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.