The function y=-16^2+50t+4 describes the height (in feet) of a discus t seconds after its released. What is the domain and range of the function?

Answer 1

y = -16t^2 + 50t + 4

It hits the ground when y=0

0 = -16t^2 + 50t + 4

8t^2 -25t -2 = 0

t = 25/16 + (1/16)sqr(625+64) = (25+26.25)/16 = 51.25/16 = 3.2 seconds

domain is t=0 to t=3.2 [3.2]

take the derivative and set it equal to zero to find maximum height

-32t +50 = 0

t = 50/32 = 25/16 = 1.5625 seconds

-16(25/16) +50(25/16) + 4 = 34(25/16) + 64/16 = (17(25)+32)/8 = 57.125 = maximum height

range is y=0 to 57.125 feet. the discus goes from 4 feet to 57 1/8 feet and back down to 0 feet