Question 839121
{{{ y = x^2 }}}
Note that {{{ y }}} must be {{{ 0 }}} 
or a positive number
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The given points are (a,b) and (c,d)
You are given that {{{ a }}} is negative
and {{{ c }}} is positive
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For the 1st point, (a,b)
{{{ y = a^2 }}}, so I can say the point is
( a, a^2 )
For the 2nd point, ( c, d ), 
{{{ y = c^2 }}}, so I can say the point is
( c, c^2 )
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Using the general point slope formula:
{{{ ( y - a^2 ) / ( x - a ) =  ( c^2 - a^2 ) / ( c - a ) }}}
Multiply both sides by {{{ ( x-a )*( c-a ) }}}
{{{ ( y - a^2 )*( c - a ) = ( c^2 - a^2 )*( x - a ) }}}
{{{ c*y - c*a^2 - a*y + a^3 = c^2*x - a^2*x - a*c^2 + a^3 }}}
{{{ ( c - a )*y = ( c^2 - a^2 )*x + c*a^2 - a*c^2  }}}
{{{ y = (( c^2 - a^2 ) / ( c - a ))*x + ( a*( a*c - c^2  )) / ( c - a ) }}}
The y-intercept is {{{ ( a*( a*c - c^2  )) / ( c - a ) }}} answer
check:
Let {{{ a = -5 }}}
Let {{{ c = 11 }}}
{{{ a^2 = 25 }}}
{{{ c^2 = 121 }}}
The points are ( -5,25 ) and ( 11, 121 ) 
{{{ ( y - a^2 ) / ( x - a ) =  ( c^2 - a^2 ) / ( c - a ) }}} 
{{{ ( y - 25 ) / ( x -(-5) ) =  ( 121 - 25 ) / ( 11 -(-5) ) }}} 
{{{ ( y - 25 ) / ( x + 5 ) = 96/16 }}}
{{{ ( y - 25 ) / ( x + 5 ) = 6 }}}
{{{ y - 25 = 6*( x + 5 ) }}}
{{{ y = 6x + 30 + 25 }}}
{{{ y = 6x + 55 }}}
This says the y-intercept is at {{{ y = 55 }}}
check:
{{{ ( a*( a*c - c^2  )) / ( c - a )  = 55 }}}
{{{ ( -5*( (-5)*11 - 11^2  )) / ( 11 -(-5) )  = 55 }}}
{{{ ( -5*( -55 - 121  )) / 16  = 55 }}}
{{{ -55 - 121 = 16*(-11) }}}
{{{ -176 = -176 }}}
OK