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=-16x^2 +50x + 4

it hits the ground when y=0

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

x = -50/-32 + or - (1/32)sqr(2500+256) =

x =(50+ or - 52.5)/32 = 102.5/32 = seconds (ignore the negative solution)

domain is 0 to 3.2 seconds rounded off to one decimal

take the derivative and set equal to zero

-32x + 50 = 0

x = 50/32 = 1.562 seconds to reach max height

-16(50/32)^2 +50(50/32) + 4 =

-2500/16 + 2500/32 + 4 =

29 feet = maximum height

range is 4 to 29 feet