To graph the equation \( y = -|x| \), let's identify some specific points on the graph.

### Key Points on the Graph
- **Vertex**: The vertex is at \((0, 0)\), where \( x = 0 \) and \( y = 0 \).

Let's calculate the values of \( y \) for different values of \( x \):

1. **For \( x = -2 \)**:
   \[
   y = -|-2| = -2
   \]
   Point: \((-2, -2)\)

2. **For \( x = -1 \)**:
   \[
   y = -|-1| = -1
   \]
   Point: \((-1, -1)\)

3. **For \( x = 0 \)**:
   \[
   y = -|0| = 0
   \]
   Point: \((0, 0)\)

4. **For \( x = 1 \)**:
   \[
   y = -|1| = -1
   \]
   Point: \((1, -1)\)

5. **For \( x = 2 \)**:
   \[
   y = -|2| = -2
   \]
   Point: \((2, -2)\)

### List of Points
The important points on the graph are:
- \((-2, -2)\)
- \((-1, -1)\)
- \((0, 0)\)
- \((1, -1)\)
- \((2, -2)\)

These points will allow you to sketch the graph accurately, forming the inverted "V" shape.

Would you like a visual graph of these points?

### Related Questions:
1. How do you find the vertex of an absolute value function?
2. How does the graph of \( y = |x| \) differ from the graph of \( y = -|x| \)?
3. How would you graph \( y = -|x| + 3 \)?
4. What effect does multiplying by a negative value have on a graph?
5. How does changing the slope inside the absolute value affect the graph?

**Tip**: When dealing with absolute value functions, the graph will always change direction at the vertex, which is a key point to identify first.

Explore how to graph the equation y = -|x| with detailed key points and a step-by-step guide. Learn about graphing absolute value functions and identifying vertex points. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation