Throwing events in track and field include the shot put, the discus throw, the hammer thro...

Throwing events in track and field include the shot put, the discus throw, the hammer throw, and the javelin throw. The distance that an athlete can achieve depends on the initial velocity of the object thrown and the angle above the horizontal at which the object leaves the hand.

In Exercises, an athlete whose event is the shot put releases the shot with the same initial velocity, but at different angles.

When the shot is released at an angle of 35°, its path can be modeled by the formula

y = −0.01x2 + 0.7x + 6.1,

in which x is the shot’s horizontal distance, in feet, and y is its height, in feet. This formula is shown by one of the graphs, (a) or (b), in the figure. Use the formula to determine the shot’s maximum distance. Use a calculator and round to the nearest tenth of a foot. Which graph, (a) or (b), shows the shot’s path?