Quadratics help

Question

The path of a soccer ball can be shown by the equation h=-4t^2+16t where h is in meters and t is in seconds
find the zeroes of the the quadratic relation
when does ball hit the ground
what is the max height of the ball

Answer 1

h=-4t^2+16t

0=-4t^2+16t

0=-4t(t-4)

t-4=0

t=4 seconds for the ball to hit the ground

 

0=-4t^2+16t

the vertex of the parabola is the maximum height

t=-b/2a where a=-4 and b=16 from the original equation

t=-16/(2*[-4])

t=-16/-8

t=2 seconds to reach maximum height

substitute 2 for t in the original equation to get h which will be the maximum height

h=-4(2^2)+16*2

h=-4(4)+32

h=-16+32

h=16 meters is the maximum height