Question 906061
{{{ y = -.005* x^2 + x + 6 }}}
Find {{{ y[max] }}}
The x-coordinate of the vertex is located at
{{{ x[max] = -b/(2a) }}}
{{{ x[max] = -1 / ( 2*(-.005) ) }}}
{{{ x[max] = 1/.01 }}}
{{{ x[max] = 100 }}}
and
{{{ y[max] = -.005* 100^2 + 100 + 6 }}}
{{{ y[max] = -50 + 106 }}}
{{{ y[max] = 56 }}} 
(a)
The max height is 56 ft
(b)
It hits the ground when {{{ y = 0 }}}
{{{ -.005* x^2 + x + 6 = 0 }}}
Multiply both sides by {{{ -200 }}}
{{{ x^2 - 200x - 1200 = 0 }}}
{{{ x^2 - 200x = 1200 }}}
{{{ x^2 - 200x + ( 200/2 )^2 = 1200 + ( 200/2 )^2 }}}
{{{ x^2 - 200x + 10000 = 11200 }}}
{{{ ( x - 100 )^2 = 11200 }}}
{{{ x  - 100 = 105.83 }}}
{{{ x = 205.83 }}}
When it hits the ground, it has traveled 205.83 ft
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Here's the plot:
{{{ graph( 600, 600, -10, 220, -5, 60, -.005*x^2 + x + 6 ) }}}