SOLUTION: Quadratic equation hidden in a word problem. A firecracker is fired straight up into the air out of a window of a building. It's height, in feet, is given by h=-16^2+136t+10, wh

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Quadratic equation hidden in a word problem. A firecracker is fired straight up into the air out of a window of a building. It's height, in feet, is given by h=-16^2+136t+10, wh      Log On


   

Question 941530: Quadratic equation hidden in a word problem.
A firecracker is fired straight up into the air out of a window of a building. It's height, in feet, is given by h=-16^2+136t+10, where t is the time, in seconds, the firecracker has been in the air
When does it reach a height of 250 feet?
at ______seconds
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
+h=-16t%5E2%2B136t%2B10
When does it reach a height of h=250 feet?
+250=-16t%5E2%2B136t%2B10
+250=-16t%5E2%2B136t%2B10
+0=-16t%5E2%2B136t%2B10-250
+0=-16t%5E2%2B136t-240....divide by 8
+0=-2t%5E2%2B17t-30
+0=-2t%5E2%2B16t%2B5t-30
+0=%28-2t%5E2%2B12t%29%2B%285t-30%29
+0=-2t%28t-6%29%2B5%28t-6%29
-1%28%282t-5%29%28t-6%29%29=0...since -1%3C%3E0, then must be
%282t-5%29%28t-6%29=0
solutions:
if %282t-5%29=0=> 2t=5 =>t=5%2F2
if %28t-6%29=0=>t=6
so, a height of 250 feet will be reached after 5%2F2 seconds when the firecracker goes up, and after 6 seconds when the firecracker goes back down