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From the image you provided, it seems like you're working on a math problem that requires plotting parabolas through sets of color-coordinated points. One parabola, corresponding to the red points, has already been plotted, and its equation is \( y = x^2 \).

To plot the remaining four parabolas (blue, green, orange, and purple), you'll need to:

1. Identify the pattern or symmetry of each set of color-coordinated points.
2. Use the vertex and other points of each set to determine the equation of the corresponding parabola.
   
### Analyzing the Points:
- **Red Parabola** is already plotted with the equation \( y = x^2 \), meaning its vertex is at \( (0,0) \), and it opens upwards.
  
For the other color-coordinated points:
- **Blue Parabola**: The points seem to be symmetric about the y-axis, and the vertex appears to be at \( (0, -4) \), meaning this is likely a vertically shifted parabola.
- **Green Parabola**: It seems to have a wider spread and might require a smaller coefficient in its equation to show that it's opening wider.
- **Orange Parabola**: This may have a similar shape to the red parabola but shifted down.
- **Purple Parabola**: Its orientation may suggest either a vertical or horizontal stretch, depending on its positioning.

### General Equation of a Parabola:
For each set of points, you can start with the general form of the quadratic equation:
\[
y = a(x - h)^2 + k
\]
Where \( (h, k) \) is the vertex of the parabola, and \( a \) determines how wide or narrow the parabola is.

Would you like assistance calculating the specific equations for each color, or help plotting them?

Plot five parabolas, one through each set of color-coordinated points.

In this challenge, plot five parabolas through color-coordinated points on a graph. Learn how to use the vertex form equation y = a(x - h)^2 + k to graph the equations of the parabolas. One parabola is provided with the equation y = x^2. Suitable for students in Grades 8-10.

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