Question 910154
The general function is:
{{{ y = a*x^2 + b*x }}}
Note that if {{{ x = 0 }}} then
{{{ y = 0 }}}, so that gives you 
the point (0,0)
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You also are given the point
(2,0), so
{{{ 0 = a*2^2 + b*2 }}}
{{{ 4a = -2b }}}
{{{ a = -b/2 }}}
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The formula for the x-coordinate of the
highest point is:
{{{ x[max] = -b/(2a) }}}
By substitution:
{{{ x[max] = ( -b/2 )*( 2/(-b)) }}}
{{{ x[max] = 1 }}}
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{{{ y[max] = a*1^2 + b*1 }}}
{{{ y[max] = a + b }}}
{{{ 1/2 = a + b }}}
and, since
{{{ a = -b/2 }}}
{{{ 1/2 = -b/2 + b }}}
{{{ 1/2 = b/2 }}}
{{{ b = 1 }}}
and
{{{ a = -b/2 }}}
{{{ a = -1/2 }}}
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So, the equation is:
{{{ y = (-1/2)*x^2 + x }}}
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Here is the plot:
{{{ graph( 400, 400, -.5, 3, -1, 2,  (-1/2)*x^2 + x ) }}}