https://file.aiquickdraw.com/mathbot/file/1726259511449y4flec9o.jpg

To determine the vertex of the absolute value function shown in the graph, let's analyze the image:

1. The graph appears to be of an absolute value function, which typically forms a "V" shape.
2. The vertex of an absolute value function is the lowest (or highest, depending on the orientation) point of the graph.
3. From the graph, we can see that the vertex is at the point where the two arms of the "V" meet. This happens at the coordinates \( (0, 4) \), based on the grid in the image.

Thus, the correct answer is **(0, 4)**.

Let me know if you would like more details or explanations.

Here are 5 related questions to deepen your understanding:
1. How do you determine the vertex of a general absolute value function \( f(x) = |x - h| + k \)?
2. What transformations would move the vertex of \( f(x) = |x| \) to the point \( (h, k) \)?
3. How does the slope of the arms of an absolute value graph change based on the equation?
4. What happens to the graph of \( f(x) = |x| \) if you multiply \( x \) by a negative constant?
5. How do the domain and range of an absolute value function change based on transformations?

**Tip:** The vertex form of an absolute value function is \( f(x) = a|x - h| + k \), where \( (h, k) \) is the vertex and \( a \) determines the steepness and direction.

What is the vertex of the absolute value function?

Learn how to find the vertex of an absolute value function from its graph. This question covers essential graphing techniques for absolute value functions and helps understand how to identify the vertex (the lowest or highest point of the graph). Suitable for high school students in Grades 9-12.

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