Question 174451
During a halftime show, a baton twirler releases her baton from a point 4 feet
 above the ground with an initial vertical velocity of 25 feet per second.
 Use a vertical motion model to write a function for the height h (in feet)
 of the baton after t seconds then graph the function and label the vertex.
:
Write an equation for this using the three elements involved here
t = time in seconds
Gravity: -16t^2, negative because it's pulling downward
Velocity upward: +25t
Initial height: 4 ft
;
h(t) = -16t^2 + 25t + 4
:
Vertex occurs at the axis of symmetry,formula for this: x = {{{(-b)/(2a)}}}

find the time of the highest point a=-16; b=25:
t = {{{(-25)/(2*-16)}}}
t = {{{(-25)/(-32)}}}
t = +.78125 sec
:
Substitute for t in the equation to find h(t)
h(t) = -16(.78125^2) + 25(.78125) + 4
h(t) = -16(.61035) + 19.53125 + 4
h(t) = -9.7656 + 23.53125
h(t) = 13.76565 ft 
:
A graph of this:
{{{ graph( 300, 200, -2, 3, -4, 20, -16x^2+25x+4) }}}
:
Did this make sense to you? Any questions?