Question 906686
{{{ h(t) = -16t^2 + 144t + 576 }}}  

this is a parabola that opens downward and its vertex is max point

{{{ graph( 600, 600, -20, 20, -20, 950,-16x^2 + 144x + 576 ) }}} 

find coordinates of vertex:

t or x-coordinate: {{{t=-b/2a}}} => {{{t=-144/2(-16)=-144/-32=4.5}}}

plug it in {{{ h(t) = -16t^2 + 144t + 576 }}} and find h or y-coordinate

{{{ h(4.5) = -16(4.5)^2 + 144*4.5 + 576 }}} 

{{{ h(4.5) = -16(20.25) + 648 + 576 }}} 

{{{ h(4.5) = -324 + 1224 }}} 

{{{ h(4.5) = 900 }}} 

so, vertex is at ({{{t}}},{{{h}}})= ( {{{4.5}}} ,{{{900}}}) and the maximum 

height of the rock is {{{h=900}}} and the time that it takes the rock to reach that maximum height is {{{4.5s}}}