A kicker punts a football from 3 feet above the ground with an initial velocity of 47 feet per second. 

Write an equation that gives the height (in feet) of the football as a function of the time (in seconds) since it was punted.

h = -16t^2 + 47t + 3

:

Find the height (in feet) of the football 2 seconds after the punt.

t=2

h = -16(2^2) + 47(2) + 3

h = -64 + 94 + 3

h = 33 ft after 2 seconds

:

Calculate how many seconds after the punt the ball would hit the ground.

h = 0

-16t^2 + 47t + 3 = 0

mult by -1, easier to factor

16t^2 - 47t - 3 = 0

Factors to

(16t+1)(t-3) = 0

the positive solution

t = 3 seconds to hit the ground

:

Graphically, (green line at 33 ft)