Question 1026235
When the form is:
{{{ f(x) = ax^2 + b*x + c }}}, then
the formula for the x-value of 
maximum height is:
{{{ x[max] = -b/(2a) }}}
{{{ f(x) = -.1x^2 + .7x + 6 }}}
{{{ x[max] = -.7 / ( 2*(-.1 )) }}}
{{{ x[max] = .7/.2 }}}
{{{ x[max] = 7/2 }}}
{{{ x[max] = 3.5 }}}
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Plug this back in to get {{{ f(x[max] ),
which is the maximum height
{{{ f(7/2) = -.1*(7/2)^2 + .7*(7/2) + 6 }}}
{{{ f(7/2) = -.1*49/4 + 4.9/2 + 6 }}}
{{{ f(7/2) = -4.9/4 + 4.9/2 + 6 }}}
{{{ f(7/2) = 4.9/4 + 24/4 }}}
{{{ f(7/2) = 28.9/4 }}}
{{{ f(7/2) = 7.225 }}}
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The maximum height is 7.225 ft
This is 3.5 ft from where it was thrown
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The ball hits the ground when {{{ f(x) = 0 }}}
{{{ f(x) = -.1x^2 + .7x + 6 }}}
{{{ -.1x^2 + .7x + 6 = 0 }}}
{{{ -x^2 + 7x + 60 = 0 }}}
{{{ ( -x + 12 )*( x + 5 ) = 0 }}}
{{{ x = 12 }}}
The ball hits the ground at 12 ft from 
where it was thrown
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check:
Here's the plot:
{{{ graph( 400, 400, -2, 15, -2, 10, -.1x^2 + .7x + 6 ) }}}