Question 805928
{{{y=-(4/9) x^2 + (24/9) x + 11}}}..here you have parabola opened upside-down and maximum is at vertex; so, find coordinates of vertex

{{{x=-b/2a}}} will give us the x-coordinate of the vertex: {{{b=(24/9)}}} and {{{a=-(4/9)}}}

{{{x=-(24/9)/2(-(4/9))}}}

{{{x=(-24/9)/(-8/9)}}}

{{{x=(-24*9)/(-8*9)}}}

{{{x=-24/-8}}}

{{{x=3}}}

now plug it in equation and find {{{y}}}


{{{y=-(4/9)3^2 + (24/9) 3 + 11}}}

{{{y=-(4/cross(9))cross(9) + (24/cross(9)3) cross(3) + 11}}}

{{{y=-4+ 24/3  + 11}}}

{{{y=-4+ 8  + 11}}}

{{{y=4  + 11}}}

{{{y=15}}} 

so,  the vertex is at:  ({{{ 3}}},{{{15}}})

since given that {{{y }}} is the maximum height of the diver, it is {{{ 15ft}}}


{{{ graph( 600, 600, -15, 15, -15, 20,-(4/9) x^2 + (24/9) x + 11) }}}