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 \( (-1, 0) \).

Would you like to see more details or have any questions?

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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.

Discover how to find the vertex of the function y = -|x + 1| with a step-by-step solution. This problem covers absolute value functions, reflections across the x-axis, and key algebraic concepts, ideal for students in Grades 7-10.

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