Answer: find the answer in the explanation.
Step-by-step explanation:
To increase the time the fireworks stays in the air by 2 seconds to build up the suspense, 2 should be added to the time t.
T + 2 = t
T = t - 2
Substitute T for t in the function g(t)
The company will make this happen without changing the length of the fuse by substituting T for t which will lead to
g(t) = -16(t - 2)^2 + 224(t - 2) + 120
How will this affect the maximum height of the firework?
Initially the function is:
g(t) = -16t2 + 224t + 120
Where the time at maximum height is found by using the formula
t = -b/2a
b = 224, a = -16
Substitutes both into the formula
t = -224/2(-16)
t = -224/-32
t = 7
Substitute 7 for t in the first equation
g(t) = -16(7)^2 + 224(7) + 120
g(t) = -16(49) + 224(7) + 120
g(t) = -784 + 1568 + 120
g(t) = 904 metres
But when the time is delayed by 2 seconds in the air, the maximum height will be
g(t) = -16( 7 - 2 )^2 + 224(7 - 2) + 120
g(t) = -16(5)^5 + 224(5) + 120
g(t) = -16(25) + 224(5) + 120
g(t) = -400 + 1120 + 120
g(t) = 840
The effect will surely reduce the maximum height of the fireworks.
