A rocket word problem

Question

A rocket is fired straight upward so that its distance in feet above the ground x seconds after firing is given by f(x)=-16x^2+400x. Remember you can find the maximum and minimum by finding the vertex. 

 

a. Find the number of seconds that it takes to reach its maximum height.

b. What is the maximum height?

Answer 1

(a)

 

That occurs at the vertex, which in this problem is at

 

x = -400/[2(-16)] s = 12.5 s

 

(b)

 

Just evaluate f(x) at x = 12.5 s and that will be the maximum height.

 

f(12.5) = ? ft

Answer 2

We can put this in vertex form.

 

f(x) = -16(x² - 25x + 625/4) + 2500

 

f(x) = -16(x - 25/2)² + 2500

 

f(x) = -16(x - 12.5)² + 2500

 

 

From the vertex, you can get your maximum height and the time it reaches its maximum height.