A football quarterback throws a long pass whose height in feet can be modeled by h(t) = -16t^2+14t+11 where t is the time in seconds.
Solve for t:
9 = -(16 t^2)+14 t+11
9 = -16 t^2+14 t+11 is equivalent to -16 t^2+14 t+11 = 9:
-16 t^2+14 t+11 = 9
Divide both sides by -16:
t^2-(7 t)/8-11/16 = -9/16
Add 11/16 to both sides:
t^2-(7 t)/8 = 1/8
Add 49/256 to both sides:
t^2-(7 t)/8+49/256 = 81/256
Write the left hand side as a square:
(t-7/16)^2 = 81/256
Take the square root of both sides:
t-7/16 = 9/16 or t-7/16 = -9/16
Add 7/16 to both sides:
t = 1 or t-7/16 = -9/16
Add 7/16 to both sides:
Answer: |t = 1 second
