The height of an arrow shot in the air is given by the function h(t)=-16t^2+144t+24, where h(t) represents the height in feet, and t represents the time in seconds.

Question

what is the maximum height of the arrow?
how long does it take to reach the maximum height?
how long does it take the arrow to hit the ground? (round to the nearest 10th of a second)
what height was the arrow shot?

Answer 1

Since you labeled it algebra rather than Calculus, I will use an algebraic solution,
completing the square

h(t) = -16(t^2 - 9t + 81/4 - 81/4) + 24
= -16( (t - 9/2)^2 - 81/4) + 24
= -16(t - 9/2)^2 + 324 + 24
= -16(t-9/2)^2 + 348

this is a downwards-opening parabola with vertex
(9/2 , 348)
It will have a maximum of 348 , when t = 9/2 or 4.5 seconds

or

the x of the vertex is -b/(2a) = -144/-32 = 4.5
h(4.5) = -16(20.25) + 144(4.5) + 24
= 348

Answer 2

Jsiaisi