Question

Quadratic Formula:
An arrow is fired into the air with an initial velocity of 96 feet per second. The height in feet of the arrow t seconds after it was shot into the air is given by the function h(x) = -16t^2 + 96t. Find the maximum height of the arrow.

Answer 1

I know how to do it using derivatives. Answer is when t = 3.

So, maximum height = -16*3^2 + 96*3 = -16*9 + 96*3 = -144 + 288 = 144 ft.

Answer 2

Quadratic way of getting to it is by finding the roots, which in this case are 0 and 6 (factoring -16t^2 + 96t gives t(-16t + 96) => t=0 or t=6). So, the maximum height will be at the vertex (midpoint of those roots where t = 3).

Answer 3

Either way...maximum height = 144ft.

Answer 4

Thank you :)