Question

A model rocket is launched straight up. Its height in feet (y) above theground x seconds after launch is modeled by the quadratic function: y =-16x2 + 200x + 15.What was the maximum height of the rocket?

Answer 1

y = - 16 x^2 + 200 x + 15

To find the maximum height, jut differentiate with respect to x

so, dy/dx = -32x + 200 = 0

x = 200/32 = 6.25

then substitute with x = 6.25 at y

So,

The maximum height = -16 * 6.25^2 + 200 * 6.25 + 15 = 640 feet

So, the maximum height of the rocket is 640 feet