A rocket fired upward from some initial distance above the ground. Its height (in feet) h, above the ground t seconds after it is fired is given by h(t)=-16t^2+160t+384 What is the rockets maximum height?

After it is fired, The rocket reaches the ground at t= seconds

Part A)

784 feet in the air (after five seconds).

Part B)

After 12 seconds.

Step-by-step explanation:

The height h (in feet) of a rocket t seconds after being fired is modeled by the function:

Part A)

We want to find the rocket's maximum height.

Since our function is a quadratic, the maximum height will occur at its vertex. The vertex of a quadratic is given by:

In this case, a = -16, b = 160, and c = 384.

So, the vertex occurs at:

The maximum height is reached after five seconds.

Then the maximum height is:

Part B)

When the rocket reaches the ground, its height h above the ground will be 0. Hence:

Solve for t. We can first divide both sides by -16:

Factor:

Zero Product Property:

Solve for each case:

Time cannot be negative. Hence, our only solution is:

The rocket reaches the ground 12 seconds after it is fired.

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step-by-step explanation:

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