Question 638864
Put the equation in the form {{{ y = ax^2 + b*x + c }}}
The x-co-ordinate of the maximum is {{{ x[max] = -b/(2a) }}}
{{{ y = -16t^2 + 52t }}}
{{{ a = -16 }}}
{{{ b = 52 }}}
{{{ t[max] = -52 / ( 2*(-16) ) }}}
{{{ t[max] = 52/32 }}}
{{{ t[max] = 1.625 }}} sec
{{{ y = -16t^2 + 52t }}}
{{{ y[max] = -16*1.625^2 + 52*1.625 }}}
{{{ y[max] = -16*2.640625 + 84.5 }}}
{{{ y[max] = -42.25 + 84.5 }}}
{{{ y[max] = 42.25 }}}
The max height is 42.25 ft
Here's the plot:
{{{ graph( 400, 400, -2, 5, -5, 50, -16x^2 + 52x ) }}}