To determine which scatter plots are best suited for a quadratic model, we need to identify the plots where the points exhibit a parabolic shape (i.e., a "U" or inverted "U" shape). A quadratic model is appropriate when the data points seem to follow a curve that opens either upwards or downwards, reflecting the general shape of a parabola.

Let's analyze each scatter plot individually based on this criterion:

1. First Plot: The data points appear to form a linear trend, not a parabolic one. Therefore, this plot is not appropriate for a quadratic model.

2. Second Plot: This plot also shows a linear pattern without any curvature, so it is not suitable for a quadratic model.

3. Third Plot: Here, the points are arranged in a pattern that resembles an upward-opening parabola. This plot would be appropriate for a quadratic model.

4. Fourth Plot: The points exhibit a pattern that could correspond to a downward-opening parabola, making it suitable for a quadratic model as well.

5. Fifth Plot: The points here don't follow a parabolic shape; they seem scattered without a clear quadratic pattern. Thus, this plot is not ideal for a quadratic model.

6. Sixth Plot: This plot shows no clear pattern and does not follow a parabolic shape, so a quadratic model is not appropriate.

Conclusion: The third and fourth plots are appropriate for a quadratic model due to their parabolic shapes.

Would you like more details on interpreting quadratic models or fitting quadratic equations to these types of plots?

Follow-up Questions

1. How can we determine if a scatter plot fits a linear, quadratic, or exponential model?
2. What are the mathematical characteristics of a quadratic function?
3. How can quadratic regression be used to fit data points to a quadratic model?
4. How does the vertex of a parabola help in identifying quadratic patterns in data?
5. How does the direction of opening (upward or downward) affect the choice of a quadratic model?

Tip

When examining scatter plots, look for symmetry and curvature patterns to quickly identify if a quadratic model may be appropriate.