Question 724176
The form of the equation is:
{{{ h = -a*t^2 + v*t + h[0] }}}
given:
{{{ h[0] = 240 }}} ft
When {{{ t = 1 }}}, {{{ h = 256 }}}
When {{{ t = 5 }}}, {{{ h = 0 }}}
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{{{ 256 = -a*1^2 + v*1 + 240 }}}
(1) {{{  -a + v  = 16 }}}
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{{{ 0 = -a*5^2 + v*5 + 240 }}}
(2) {{{ 25a - 5v = 240 }}}
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(2) {{{ 5a - v = 48 }}}
Add (1) and (2)
(1) {{{  -a + v  = 16 }}}
(2) {{{ 5a - v = 48 }}}
{{{ 4a = 64 }}}
{{{ a = 16 }}}
and, since
(1) {{{  -a + v  = 16 }}}
(1) {{{  -16 + v  = 16 }}}
(1) {{{ v = 32 }}}
The equation is:
{{{ h = -16t^2 + 32t + 240 }}}
Here's the plot:
{{{ graph( 400, 400, -1, 6, -20, 280,  -16x^2 + 32x + 240 ) }}}