A quadratic model fits a scatterplot that rises to a peak and then falls in a roughly mirror-image pattern. Read well-spaced points at the start, peak, and end, then enter them in a Desmos table for a quadratic regression. Checking only the peak is risky: several curves can reach it while missing an endpoint.
Hints
- Hint 1
Equal heights at two different weeks put the axis of symmetry, the curve’s vertical mirror line, halfway between them. Find the first and last dots at about the same height. Which week lies halfway between them?
- Hint 2
Use the two ends and the highest dot as three well-spaced points. A quadratic has three coefficients, the numbers that set its bend and position, so these points give Desmos the curve’s start, peak, and end.
- Hint 3
Put weeks in and baskets in , then fit . The tilde tells Desmos to fit a curve to the dots rather than demand that every measured dot lie exactly on it.
Step-by-step
Fit the ends and the peak
Step 1Read three landmarks from the plot
At weeks and , the plot shows about baskets each, so the axis of symmetry, the parabola’s mirror line, runs midway at week . The highest dot is about . Both ends and the peak anchor the curve.
- Step 2
Pair the weeks with their basket counts
Enter , , and in a Desmos table, with weeks in and basket counts in . Desmos shows three paired rows, one for each dot. These well-spaced points capture the start, peak, and end instead of overfocusing on one part of the plot.
- Step 3
Fit and read the quadratic equation
Type . The regression finds the quadratic that fits the table; under PARAMETERS, Desmos reports , , and . With as week and as baskets harvested, the model is . Choice A.