Question 937418
You are given the points:
( 0,0 )
( 50,0 )
The max height occurs halfway
between the horizontal
co-ordinates, so you also have:
( 25,24 ) 
Note that {{{ 8 }}} yds  = {{{ 24 }}} ft
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The equation is in the form:
{{{ h(x) = -a*x^2 + b*x + c }}}
( 0,0 )
{{{ 0 = -a*0^2 + b*0 + c }}}
{{{ c = 0 }}}
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( 50,0 )
{{{ 0 = -a*50^2 + b*50 }}}
{{{ 2500a = 50b }}}
{{{ 50a = b }}}
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( 25,24 )
{{{ 24 = -a*25^2 + b*25 }}}
{{{ 24 = -a*625 + 25b }}}
{{{ 625a = 25b - 24 }}}
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By substitution:
{{{ 625a = 25*50a - 24 }}}
{{{ 625a = 1250a - 24 }}}
{{{ 625a = 24 }}}
{{{ a = .0384 }}}
{{{ b = 50a }}}
{{{ b = 1.92 }}}
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{{{ h(x) = -.0384x^2 + 1.92x }}} answer
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check:
Does it go through ( 50,0 ) ?
{{{ h(50) = -.0384*50^2 + 1.92*50 }}}
{{{ h(50) = -.0384*2500 + 96 }}}
{{{ h(50) = -96 + 96 }}}
OK
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Does it go through ( 25,24 )?
{{{ h(25) = -.0384*25^2 + 1.92*25 }}}
{{{ h(25) = -24 + 48 }}}
{{{ h(25) = 24 }}}
OK