The height in feet of a rocket after t seconds is given by h(t) = 160t - 16t^2.

find the maximum height the rocket attains in feet

Step-by-step explanation:

h(t)=160t-16t^2=-16(t²-10t+25-25)

=-16(t-5)²+400

max. height reached=400 ft

The maximum height 400 feet is attained at t = 5 seconds.

Step-by-step explanation:

All powers of in the equation for are integers that are greater than or equal to zero. Additionally, the greatest power of is two. Hence, is a quadratic equation about .

In this case,

The question is asking for the maximum value of this equation. Start by finding the (time) that would maximize the value of the polynomial.

The graph of a quadratic equation looks like a parabola. Additionally, since the coefficient of is less than zero, the parabola opens downward. The maximum value of the parabola would be at its vertex. Additionally, at the vertex,

.

In other words, the rocket is at its maximum height when time is equal to 5 seconds.

To find that height, let and evaluate :

.

That is: the maximum height of the rocket would be 400 feet.

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step-by-step explanation: