A pilot of a helicopter plans to release a bucket of water on a forest fire. The height y in feet of water t seconds after its release is modeled by y=−16t2−2t+400 . How long will it take for the water to reach the ground? round to the nearest decimal.

You’re gonna have to use the quadratic formula here and a bit of thinking. We know y is height, and once it touches the ground, it will be 0.

(-b +- sqrt b^2 - 4ac)/2a
2 +- sqrt(4 + 48(400))/-32
(2 +- 138.58)/-32
We don’t want a negative time because it’ll make no sense. So do subtraction

(2-138.58)/-32 = 4.27 seconds aka 4.3 seconds