If a football player passes a football from 4 feet off the ground with an initial velocity of 36 feet per second, how long will it take the football to hit the ground? use the equation h = -16t^2 + 6t +4. round your answer to the nearest hundredth.

t = 0.722 seconds

Step-by-step explanation:

Given in the question that an equation

h = -16t² + 6t + 4

here h is the height

        t is the time

To solve this question we need to substitute height with zero because at ground level height is zero

0 = -16t² + 6t + 4

a = -16

b = 6

c = 4

Formula to use

t = -b±√(b²-4ac) / 2a

Plug values in the formula

t = -6 ± √36-4(-16)(4) / 2(-16)

t =  6±2√73 / 32

t =  6+2√73 / 32 or t =  6-2√73 / 32

t = 0.722 or t = -0.347

since time can't be in negative so we reject  t = -0.347

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.