A ball is thrown vertically upward with an initial velocity of 80 ft. per second. The distance s (in ft.) of the ball from the ground after t seconds is given by the function s(t)=80t-16t^2.
[spoiler]a) in what time interval is the ball more than 96ft above the ground?
s(t) = 96 ft
96 = 80t - 16t^2
96 = -16 (t^2-5t)
-6= (t^2 - 5t)
t^2 - 5t + 6
(t-3)(t-2)
t= 3 and t= 2
b) What is the maximum height of the ball ?
** Hindi ako sure
s(t) = 80t - 16t^2 or --> s(t)= -16t^2 + 80t
standard formula for vertex: f(x) = a(x-h)^2 +k
simplified: f(x)= a (x^2 - 2xh + h^2)
finding the constant (aka h^2): -2xh/2x = -h then i-square. XD -> h^2
vertex is (h,k)
s(t) = -16 (t^2 - 5t) <-- maglalagay ng constant bale...
-5t/2t = (-5/2)^2 = 25/4
equation: s(t) = -16(t^2 - 5t +25/4)
pero dpat even equation, maglalagay din ng 25/4 sa kbila. kasama din yung (-16)
s(t) - (16)(25/4) = -16(t^2 - 5t +25/4)
s(t) -100 = -16(t^2 - 5t +25/4)
*transpose. s(t) = -16(t^2 - 5t +25/4) + 100
* factor out expression
s(t) = -16 (t-5/2)^2 + 100 --> standard equation --> f(x) = a(x-h)^2 +k
vertex; (h,k)--> (5/2, 100)
max height; 100ft[/spoiler]
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