Again, the quarterback throws the football, but this time the model y = –16x2 + 35x + 6.5 describes the height (y), in feet, of the football x seconds after it is thrown. If the ball is not caught, how long will it be in the air?
The model is:y = - 16 x² + 35 x + 6.5At x = 0; y ( 0 ) = 6.5 ft.We have to find the zeroes of the parabola:x 1/2 = ( - 35 +/- √(35² - 4 · ( -16 ) · 6.5 ) ) / ( - 32 ) = = ( - 35 */- √1641 ) / ( - 32 ) = = ( - 35 +/- 40.5 ) / ( - 32 ) x 1 = - 0.17x 2 = 2.36The ball will be in the air from x = 0 s to x = 2.36 s.Answer: 2.36 s.
