Question 735792
The equation has the general form {{{ y = ax^2 + b*x + c }}}
The x-coordinate of the vertex is at {{{ x = -b/(2a) }}}
In the given equation:
{{{ t = -64 / ( 2*(-16)) }}}
{{{ t = 2 }}}
(a) The rocket takes 2 sec to reach maximum height
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Find {{{s}}} when {{{ t = 2 }}}
{{{ s = -16t^2 + 64t + 512 }}}
{{{ s = -16*2^2 + 64*2 + 512 }}}
{{{ s = -64 + 128 + 512 }}}
{{{ s = 576 }}}
(b) At the vertex, the height is 576 ft above ground
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Find {{{ t }}} when {{{ s = 0 }}}
{{{ 0 = -16t^2 + 64t + 512 }}}
{{{ -t^2 + 4t + 32 }}}
{{{ ( -t + 8 )*( t + 4 ) }}} ( I could see these were factors )
{{{ t = 8 }}} ( ignore other solution-can't have negative time )
(c) In 8 sec, the rocket reaches the ground
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Here's the plot:
{{{ graph( 400, 400, -3, 10, -30, 625, -16x^2 + 64x + 512 ) }}}