A suitable model for the motion of the tennis ball is a smooth, symmetric curve shaped like an "upside-down U" (a parabola). This curve starts at the point (0,0), rises to a single maximum point near (1,5), and then descends back to (2,0), matching the pattern of the plotted data.
This curve is different from a straight line in several important ways:
The slope (rate of change) is positive for t<1, meaning the height increases as time increases.
At the top of the curve, around t≈1, the slope is zero. This is called a "turning point" or "vertex," where the ball reaches its maximum height before starting to fall.
For t>1, the slope is negative, so the height decreases as time increases.
A straight line would have a constant slope and could not model the ball's rise and fall. The presence of a single turning point and the change in slope are key features that distinguish this curve from a straight line.