The height h (in feet) of a certain rocket t seconds after it leaves the ground is modeled by LaTeX: h/left (t/right) / : =/:-16t^2+64t+12. h (t) = - 16 t 2 + 64 t + 12. How long does it take the rocket to reach the maximum height?

76 feet

Step-by-step explanation:

h = - 16t^2 + 64t + 12

The maximum height will be reached after - b/2a secs

a = - 16, b = 64, c = 12

-b/2a = - 64/2 (-16)

= - 64/-32

= 2 secs

The maximum height = - 16 (2) ^2 + 64 (2) + 12

= - 16 (4) + 128 + 12

= - 64 + 128 + 12

= 76 ft