To find the vertex of the function $y = -|x + 1|$, we need to analyze the equation step by step.

Step 1: Understand the Structure

The equation $y = -|x + 1|$ is a modification of the absolute value function $y = |x + 1|$, which is V-shaped and has its vertex at the point where the expression inside the absolute value equals zero.

Step 2: Find the Vertex of $y = |x + 1|$

The expression inside the absolute value is $x + 1$. To find the x-coordinate of the vertex: $x + 1 = 0 \quad \Rightarrow \quad x = -1$ At $x = -1$, $y = |x + 1|$ is minimized, so the vertex of the original function $y = |x + 1|$ is at $(-1, 0)$.

Step 3: Apply the Negative Sign

The negative sign outside the absolute value reflects the graph of $y = |x + 1|$ across the x-axis. Therefore, the vertex of the function $y = -|x + 1|$ will also be at $x = -1$, but the y-coordinate will be the negative of what it was: $y = -|x + 1| = -|(-1) + 1| = 0$

Final Answer

The vertex of the function $y = -|x + 1|$ is at $(-1, 0)$.

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Here are 5 related questions:

1. How do you find the vertex of a function like $y = -|x + 2| + 3$?
2. What is the vertex of $y = |x - 4| - 5$?
3. How would the graph of $y = -|x + 1| + 2$ differ from $y = -|x + 1|$?
4. What are the general properties of absolute value functions?
5. How does reflecting an absolute value function across the x-axis affect its vertex?

Tip: When dealing with absolute value functions, always identify the point where the expression inside the absolute value equals zero; this will help you find the vertex.