Atoy rocket launched straight up from the ground with an initial velocity of 80 ft/s returns to the ground after 5 s. the height of the rocket t seconds after launch is modeled by the function f(t)=−16t2+80t . what is the maximum height of the rocket, in feet?

Maximum height oh the rocket was 100 feet.

Step-by-step explanation:

It has been given in the question that rocket follows the function f(t) = 80t-16t² where t is the time taken by rocket to reach maximum height and coming back to the ground.

Since initial velocity of the rocket is = 80 ft/sec

and total time taken by the rocket to come back to the ground is 5 sec

time taken by the rocket to reach the maximum height = 5/2 = 2.5 sec

Therefore from the given function

Maximum height achieved by the rocket = 80.(2.5) - 16.(2.5)²

= 200 - 100 = 100 ft.

you need a common difference between consecutive terms to be constant, like 1,2,3,4 or 2,4,6,8, or 1,3,6,9

both equations and proportions are better.