The height , h, in feet, of a bottle rocket is modeled by:



where t is the time in seconds.

A. Factor the expression.

B. What is the height of the rocket after 2 seconds?

C. What is the height of the rocket after 3.75 seconds? Explain the solution.

A. To factor the expression, we need to rewrite it as a multiplication of its factors.

The expression given is:

h = -16t^2 + 64t

We can see that both terms have a common factor of 16t. Therefore, we can factor it out:

h = 16t(-t + 4)

So, the factored expression is:

h = 16t(-t + 4)

B. To find the height of the rocket after 2 seconds, we substitute t = 2 into the expression:

h = 16(2)(-2 + 4)
= 16(2)(2)
= 64 feet

Therefore, the height of the rocket after 2 seconds is 64 feet.

C. To find the height of the rocket after 3.75 seconds, we substitute t = 3.75 into the expression:

h = 16(3.75)(-3.75 + 4)
= 16(3.75)(0.25)
= 15(0.25)
= 3.75 feet

We can explain the solution as follows:

At time t = 3.75 seconds, the rocket has reached a height of 3.75 feet. This is calculated by substituting the given time into the expression and performing the necessary calculations. The rocket reaches its maximum height and starts descending after this time.