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)=−16t^2+80t . what is the maximum height of the rocket, in feet? enter your answer in the box.

The height of the rocket is modeled by the function:



If we observe this equation, we see that the function is quadratic. The shape of the quadratic function is parabolic and the maximum or minimum value of a parabola always lies at its vertex. In the given function, since the co-efficient of leading term (t²) is negative, so this parabola will have a maximum value at its vertex. 

The vertex of parabola is given by: 



b is the coefficient of t term. So b = 80
a is the coefficient of squared term. So a= - 16

So,



This means at 2.5 sec the height of rocket will be maximum. The maximum height will be:



Therefore, the maximum height of the rocket will be 100 feet. 

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