https://file.aiquickdraw.com/mathbot/file/17381231674707m724yl1.jpg

The given equation is:

\[
y = -|x - 3|
\]

This represents an absolute value function that is flipped vertically due to the negative sign. The vertex of this function is at \( (3,0) \), which means the graph should have its lowest point at \( (3,0) \) and open downward.

However, the provided graph shows an absolute value function opening upwards, which corresponds to \( y = |x - 3| \) rather than \( y = -|x - 3| \). This indicates that the graph is incorrect for the given equation.

Would you like a detailed explanation on how to correctly plot this function? Here are five follow-up questions to deepen your understanding:

1. How do transformations affect the graph of an absolute value function?
2. What is the effect of a negative sign in front of the absolute value function?
3. How can we determine the vertex of an absolute value function?
4. How can we verify if a given graph matches an equation?
5. What is the domain and range of the function \( y = -|x - 3| \)?

**Tip:** The vertex of an absolute value function \( y = a |x - h| + k \) is always at \( (h, k) \).

Learn how to graph the absolute value function y = -|x - 3|, including transformations and vertex identification. This problem covers key algebraic concepts such as reflections, shifts, and domain-range analysis. Suitable for students in Grades 8-10.

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