Question 763418
Here's the graph:
{{{ graph( 400, 400, -4, 16, -100, 1000, -25x^2 + 300x ) }}}
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One thing to notice right away is it must go through
( 0,0 ) since making {{{ x = 0 }}} will force {{{ y = 0 }}}
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The x-crossings ( the roots ) are at ( 0,0 ) and ( 12,0 )
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The vertex is at {{{ -b/(2a) }}} when the equation has the form
{{{ y = ax^2 + bx + c }}}
For your equation:
{{{ a = -25 }}}
{{{ b = 300 }}}
{{{ c = 0 }}}
{{{ -b/(2a) = -300 / ( 2*(-25)) }}}
{{{ -b/(2a) = -300 / (-50) }}}
{{{ -b/(2a) = 6 }}}
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So, the vertex is at ( 6,y ) Now find {{{ y }}}
{{{ y = -25*6^2 + 300*6 }}}
{{{ y = -900 + 1800 }}}
{{{ y = 900 }}}
The vertex is at ( 6,900 ) 
The vertex is above the x-crossings, so it 
must open down.