https://file.aiquickdraw.com/mathbot/file/1727713236115xvh54e7z.jpg

The given equation is \( y = -x^2 \), which represents a downward-facing parabola because of the negative sign in front of \( x^2 \). 

### Steps to plot the points:

1. **Vertex**: 
   The vertex of this parabola is at \( (0, 0) \), as the equation is in the standard form \( y = ax^2 + bx + c \), where \( a = -1 \), \( b = 0 \), and \( c = 0 \).

2. **Choose points to the left and right of the vertex**:
   To the left of the vertex (where \( x = -1 \) and \( x = -2 \)):
   - When \( x = -1 \): 
     \[
     y = -(-1)^2 = -1
     \]
     So, the point is \( (-1, -1) \).
   - When \( x = -2 \): 
     \[
     y = -(-2)^2 = -4
     \]
     So, the point is \( (-2, -4) \).

   To the right of the vertex (where \( x = 1 \) and \( x = 2 \)):
   - When \( x = 1 \): 
     \[
     y = -(1)^2 = -1
     \]
     So, the point is \( (1, -1) \).
   - When \( x = 2 \): 
     \[
     y = -(2)^2 = -4
     \]
     So, the point is \( (2, -4) \).

### Points to plot:
1. Vertex: \( (0, 0) \)
2. To the left: \( (-1, -1) \) and \( (-2, -4) \)
3. To the right: \( (1, -1) \) and \( (2, -4) \)

If you were graphing, these points form a symmetric shape around the vertex \( (0, 0) \), characteristic of a parabola.

Would you like more details or any further questions?

### Here are 5 related questions for practice:
1. What is the general form of a quadratic equation?
2. How does the sign of the coefficient \( a \) in \( y = ax^2 \) affect the orientation of the parabola?
3. How can you find the vertex of a parabola if it is not at the origin?
4. How do you determine the axis of symmetry for a parabola?
5. How do you calculate the y-intercept and x-intercepts of a parabola?

**Tip**: The axis of symmetry of a parabola \( y = ax^2 + bx + c \) is given by the formula \( x = -\frac{b}{2a} \).

Graph the parabola y = -x^2 and plot five points: the vertex, two points to the left of the vertex, and two points to the right of the vertex.

Learn how to graph the parabola y = -x^2 by plotting the vertex and key points. This problem covers essential quadratic equation concepts, focusing on graphing and symmetry. Suitable for students in Grades 7-9.

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