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?