<PRE><B>Question 652685</B>
A Little League baseball player throws a ball upward. The height h of the ball (in feet) t seconds after the ball is released is given by the quadratic equation
h = -16t2 +30t +4

a)	How long does it take the ball to reach a height of 18ft?
set h to 18 and solve for t:
h = -16t^2 +30t +4
18 = -16t^2 +30t +4
0 = -16t^2 +30t - 14
0 = 16t^2 -30t + 14
0 = 8t^2 -15t + 7
0 = 8t^2 -8t -7t + 7
0 = (8t^2 -8t) - (7t - 7)
0 = 8t(t-1) - 7(t-1)
0 = (t-1)(8t-7)
t = {1, 7/8}
t = {1, 0.875}
it reaches 18 ft twice.  Once at 0.875 sec (going up) and again at 1 sec (going down).
.
b)	How long does it take the ball to hit the ground?
set h to 0 and solve for t:
h = -16t^2 +30t +4
0 = -16t^2 +30t +4
0 = 16t^2 -30t -4
0 = 8t^2 -15t -2
0 = 8t^2 -16t+t -2
0 = (8t^2-16t) + (t-2)
0 = 8t(t-2) + (t-2)
0 = (t-2)(8t+1)
t = {-1/8, 2}
we can throw out the negative solution leaving:
t = 2 seconds

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