A scatterplot that rises and then falls suggests a quadratic model shaped like an upside-down arch. To choose among similar equations, read a point near an edge of the plot, where their predictions may differ more than they do at the peak. Substitute that input into each choice in Desmos, then check the closest model against another point. A good model follows the whole pattern, not just the peak.
Hints
- Hint 1
Each dot pairs a temperature with a swimmer count. Near degrees Celsius, the plot shows about hundred swimmers. What does each equation predict at that temperature?
- Hint 2
A model is a prediction, so it need not pass through every dot. After comparing predictions at , check whether the closest equation also reaches about the observed peak near .
Step-by-step
Test the models at two temperatures
Step 1Pick points that show the curve's shape
The dots rise to about and then fall, so a downward-opening parabola matches their overall shape. At the left edge, the dot is about . Use to separate the choices, then check the model you favor near the peak. The -values are in hundreds of swimmers.
- Step 2
Compare all four predictions at the left edge
Type , then type each choice with in place of . Desmos prints , , , and , in choice order. The observed value is about , so is closest. In particular, don't pick the equation that predicts because it also looks close to the peak.
- Step 3
Check the peak and choose
Keep those lines and type . Desmos prints , close to the plotted peak of about hundred swimmers. So fits both the edge and the peak of the swimmer data. Choice A.