https://file.aiquickdraw.com/mathbot/file/1729120888807dnsnqymb.jpg

The equation in the image is \( y = -2x^2 \), which represents a parabola. Let's break this down:

### Step 1: Identifying the Vertex
The vertex form of a parabola is \( y = a(x - h)^2 + k \). In this case, \( a = -2 \), and since there is no \( h \) or \( k \) (meaning \( h = 0 \) and \( k = 0 \)), the vertex is at \( (0, 0) \).

### Step 2: Plot Points Around the Vertex
You are asked to plot the vertex and two points on each side of it.

1. **Vertex**: \( (0, 0) \)

Now, let's calculate two points to the left and two points to the right of the vertex by plugging in \( x \)-values:

- For \( x = -2 \):
  \[
  y = -2(-2)^2 = -2(4) = -8 \quad \Rightarrow \quad (-2, -8)
  \]
  
- For \( x = -1 \):
  \[
  y = -2(-1)^2 = -2(1) = -2 \quad \Rightarrow \quad (-1, -2)
  \]

- For \( x = 1 \):
  \[
  y = -2(1)^2 = -2(1) = -2 \quad \Rightarrow \quad (1, -2)
  \]

- For \( x = 2 \):
  \[
  y = -2(2)^2 = -2(4) = -8 \quad \Rightarrow \quad (2, -8)
  \]

### Step 3: Summary of the Points
The five points to plot on the graph are:
- \( (-2, -8) \)
- \( (-1, -2) \)
- \( (0, 0) \) (vertex)
- \( (1, -2) \)
- \( (2, -8) \)

Would you like more details on how these points are plotted or any further clarification?

Here are 5 related questions:
1. How does the coefficient \( a = -2 \) affect the direction and shape of the parabola?
2. What is the axis of symmetry for this parabola?
3. How would the graph change if the equation was \( y = 2x^2 \) instead of \( y = -2x^2 \)?
4. How can you find the focus and directrix of the parabola from the given equation?
5. Can you identify how the vertex changes if we modify the equation to include \( h \) and \( k \)?

**Tip**: For any quadratic function \( y = ax^2 \), the value of \( a \) determines whether the parabola opens upwards (if \( a > 0 \)) or downwards (if \( a < 0 \)).

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

This page explains how to plot five points on the parabola y = -2x^2, including the vertex and two points to the left and right of the vertex. Step-by-step instructions show how to calculate these points and explain their significance for graphing quadratic functions. Suitable for students in Grades 9-11.

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