Susan throws a softball upward into the air at a speed of 32

Susan throws a softball upward into the air at a speed of 32 feet per second from a 8-foot platford. The distance upward that the ball travels is given by the function d(t)= -16t^2+32t+8. What is the maximum height of the softball? How many seconds does it take to reach the ground after first being thrown upward? ( Round anwer to nearest tenth)

Please explain :)

Solution

d(t)= -16t^2+32t+8

Maximum height of quadratice function is attained at vertex (h, k):

ax^2 +bx +c ;h = -b/2a k= f(h)

d(t)= -16t^2+32t+8

t = -32/(2*(-16)) = 1 sec

d(1) = -16 +32 +8 = 24 feet maxium height of softball

How many seconds does it take to reach the ground after first being thrown upward?

--- ground : d(t) =0

-16t^2+32t+8 =0

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

factorise :-2t^2 +4t +2 =0

use quadratic formula:

t = (-2 +/- sqrt(16 + 16)/-4

= (-2 +/- 4sqrt2/-4

= 0.5 +/- sqrt2

Neglect -ve root

t = 0.5 +sqrt2 = 1.914 sec to reach ground