Aflare was launched up from the ground with an initial velocity of 176 feet per second (ft/s). the height of the flare t seconds after launch is modeled by the function f(t)=−16t2+176t. how long was the flare in the air before it hit the ground?

The equation f(t) = -16t² + 176t is a quadratic equation, and so its maximum must be found at its vertex. In order to get this, you can use the formula 
t = -b/2a.
Substituting, we have:
t = -176/2(-16) = 5.5 seconds. 
But this is just only the time needed for the flare to reach its maximum height. To solve for the time the flare has been in the air, we multiply the maximum height by 2.

2 x 5.5 seconds = 11 seconds.