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The equation in the image provided is \( y = -3x^2 \), and you are asked to plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex.

### Step-by-step:

1. **Vertex of the Parabola**:
   The equation is of the form \( y = ax^2 \), where \( a = -3 \). In this case, the parabola opens downwards because \( a < 0 \), and the vertex is at \( (0, 0) \) because there's no shift in the \( x \)- or \( y \)-directions.

2. **Choosing Points**:
   To plot five points, we need to choose two points to the left of the vertex (negative \( x \)-values) and two points to the right (positive \( x \)-values).

3. **Calculating the Points**:
   We will plug in \( x = -2, -1, 0, 1, 2 \) into the equation to get the corresponding \( y \)-values.

   - For \( x = -2 \):
     \[
     y = -3(-2)^2 = -3(4) = -12
     \]
     Point: \( (-2, -12) \)
   
   - For \( x = -1 \):
     \[
     y = -3(-1)^2 = -3(1) = -3
     \]
     Point: \( (-1, -3) \)
   
   - For \( x = 0 \):
     \[
     y = -3(0)^2 = 0
     \]
     Point: \( (0, 0) \) (vertex)

   - For \( x = 1 \):
     \[
     y = -3(1)^2 = -3
     \]
     Point: \( (1, -3) \)
   
   - For \( x = 2 \):
     \[
     y = -3(2)^2 = -12
     \]
     Point: \( (2, -12) \)

4. **Final Points**:
   - \( (-2, -12) \)
   - \( (-1, -3) \)
   - \( (0, 0) \) (vertex)
   - \( (1, -3) \)
   - \( (2, -12) \)

### Graphing:
You can now plot these points on a graph, which will form a symmetric, downward-opening parabola centered at \( (0, 0) \).

Would you like to go into more details or have any questions?

Here are five follow-up questions:
1. How does the value of \( a \) in \( y = ax^2 \) affect the shape of the parabola?
2. What is the effect of adding constants to \( x \) or \( y \) in the equation of a parabola?
3. How can you determine if a parabola opens upwards or downwards from its equation?
4. What is the significance of the vertex in a parabolic equation?
5. How can you find the axis of symmetry for a given parabola?

**Tip**: The vertex form of a parabola is \( y = a(x - h)^2 + k \), where \( (h, k) \) is the vertex. This form makes it easier to identify transformations.

Graph the parabola for the equation y = -3x^2 and plot five points, including the vertex and two points on either side of the vertex.

Learn how to graph the parabola y = -3x^2 by plotting five points, including the vertex and symmetrical points to the left and right. This step-by-step solution is suitable for students in Grades 8-10 and covers key concepts like quadratic functions and parabolas.

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