Question

The path of a flying fish as it made its approach to the surface of the ocean and flew out of the water is represented by the quadratic function h(t) = -t2 + 6t - 5, where t represents the time, in seconds, and h(t) represents the fish's height and depth, in feet. Graph the function using the graphing calculator. To the nearest second, how long was the fish out of the water?

1 second
3 seconds
4 seconds
5 seconds

Answer 1

h(t) = -t^2 + 6t - 5. Set h(t)=0 to find when it crosses the surface:

-t^2 + 6t - 5 = 0 → t^2 - 6t + 5 = 0 → (t - 1)(t - 5) = 0

So t = 1 s (leaves water) and t = 5 s (re-enters). Time out of the water = 5 − 1 = 4 seconds.

Answer: 4 seconds.