Question 691053
how long does it take a ball to reach maximum height with the formula h=-16t^2+24t+30 where h= height and t=seconds
:
The max height occurs at the axis of symmetry which we can find with the formula x = -b/(2a)
In this equatio
t = {{{(-24)/(2*-16)}}}
t = {{{(-24)/(-32)}}}
t = +.75 seconds to reach max height
:
To find max height, replace t with .75
h = -16(.75^2) + 24(.75) + 30
h = -16(.5625) + 18 + 30
h = -9 + 18 + 30
h = 39 ft is max height occurring .75 seconds after launch
:
Here is a graph of that equation, showing this very clearly
{{{ graph( 300, 200, -2, 3, -10, 50, -16x^2+24x+30) }}}