SOLUTION: A firecracker is fired straight up into the air out of a window of a building. Its height, in feet, is given by h = -16 t^2 + 88 t + 230, where t is the time, in seconds, the fircr

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Question 864335: A firecracker is fired straight up into the air out of a window of a building. Its height, in feet, is given by h = -16 t^2 + 88 t + 230, where t is the time, in seconds, the fircracker has been in the air.
When does it reaches a height of 350 feet?
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Given;
(1) h = -16t^2 + 88t +230 and we want to know the t when h = 350. So let h = 350 and get
(2) 350 = -16t^2 + 88t +230 or
(3) -16t^2 + 88t +230 - 350 = 0 or
(4) -16t^2 + 88t - 120 = 0 or
(5) -2t^2 + 11t - 15 = 0
Now use the quadratic solution formula to get
(6) t = (11 +- 1)/4 or
(7) t = {3,2.5}
Let t = 3 in (1) to check the answer.
Is (350 = -16*3^2 + 88*3 + 230)?
Is (350 = -16*9 + 264 + 230)?
Is (350 = 494 - 144)?
Is (350 = 350)? Yes
Answer: The firecracker reaches 350 ft at t = 2.5 seconds and 3 seconds. Note it reaches a peak of 351 ft at 2.75 seconds (half way between 2.5 and 3).