document.write( "Question 839121: 2 points are chosen on the parabola defined by y=x^2, one with a positive x-coordinate and the other with a negative x-coordinate. If the points are (a,b) and (c,d), where a < 0 and c > 0, find the y-intercept of the line joining the 2 points in terms of a and c \n" ); document.write( "

Algebra.Com's Answer #505548 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+y+=+x%5E2+\"$
\n" ); document.write( "Note that $\"+y+\"$ must be $\"+0+\"$
\n" ); document.write( "or a positive number
\n" ); document.write( "-----------------------------
\n" ); document.write( "The given points are (a,b) and (c,d)
\n" ); document.write( "You are given that $\"+a+\"$ is negative
\n" ); document.write( "and $\"+c+\"$ is positive
\n" ); document.write( "---------------------------------
\n" ); document.write( "For the 1st point, (a,b)
\n" ); document.write( " $\"+y+=+a%5E2+\"$ , so I can say the point is
\n" ); document.write( "( a, a^2 )
\n" ); document.write( "For the 2nd point, ( c, d ),
\n" ); document.write( " $\"+y+=+c%5E2+\"$ , so I can say the point is
\n" ); document.write( "( c, c^2 )
\n" ); document.write( "-----------------------------------
\n" ); document.write( "Using the general point slope formula:
\n" ); document.write( " $\"+%28+y+-+a%5E2+%29+%2F+%28+x+-+a+%29+=++%28+c%5E2+-+a%5E2+%29+%2F+%28+c+-+a+%29+\"$
\n" ); document.write( "Multiply both sides by $\"+%28+x-a+%29%2A%28+c-a+%29+\"$
\n" ); document.write( " $\"+%28+y+-+a%5E2+%29%2A%28+c+-+a+%29+=+%28+c%5E2+-+a%5E2+%29%2A%28+x+-+a+%29+\"$
\n" ); document.write( " $\"+c%2Ay+-+c%2Aa%5E2+-+a%2Ay+%2B+a%5E3+=+c%5E2%2Ax+-+a%5E2%2Ax+-+a%2Ac%5E2+%2B+a%5E3+\"$
\n" ); document.write( " $\"+%28+c+-+a+%29%2Ay+=+%28+c%5E2+-+a%5E2+%29%2Ax+%2B+c%2Aa%5E2+-+a%2Ac%5E2++\"$
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\n" ); document.write( "The y-intercept is $\"+%28+a%2A%28+a%2Ac+-+c%5E2++%29%29+%2F+%28+c+-+a+%29+\"$ answer
\n" ); document.write( "check:
\n" ); document.write( "Let $\"+a+=+-5+\"$
\n" ); document.write( "Let $\"+c+=+11+\"$
\n" ); document.write( " $\"+a%5E2+=+25+\"$
\n" ); document.write( " $\"+c%5E2+=+121+\"$
\n" ); document.write( "The points are ( -5,25 ) and ( 11, 121 )
\n" ); document.write( " $\"+%28+y+-+a%5E2+%29+%2F+%28+x+-+a+%29+=++%28+c%5E2+-+a%5E2+%29+%2F+%28+c+-+a+%29+\"$
\n" ); document.write( " $\"+%28+y+-+25+%29+%2F+%28+x+-%28-5%29+%29+=++%28+121+-+25+%29+%2F+%28+11+-%28-5%29+%29+\"$
\n" ); document.write( " $\"+%28+y+-+25+%29+%2F+%28+x+%2B+5+%29+=+96%2F16+\"$
\n" ); document.write( " $\"+%28+y+-+25+%29+%2F+%28+x+%2B+5+%29+=+6+\"$
\n" ); document.write( " $\"+y+-+25+=+6%2A%28+x+%2B+5+%29+\"$
\n" ); document.write( " $\"+y+=+6x+%2B+30+%2B+25+\"$
\n" ); document.write( " $\"+y+=+6x+%2B+55+\"$
\n" ); document.write( "This says the y-intercept is at $\"+y+=+55+\"$
\n" ); document.write( "check:
\n" ); document.write( " $\"+%28+a%2A%28+a%2Ac+-+c%5E2++%29%29+%2F+%28+c+-+a+%29++=+55+\"$
\n" ); document.write( " $\"+%28+-5%2A%28+%28-5%29%2A11+-+11%5E2++%29%29+%2F+%28+11+-%28-5%29+%29++=+55+\"$
\n" ); document.write( " $\"+%28+-5%2A%28+-55+-+121++%29%29+%2F+16++=+55+\"$
\n" ); document.write( " $\"+-55+-+121+=+16%2A%28-11%29+\"$
\n" ); document.write( " $\"+-176+=+-176+\"$
\n" ); document.write( "OK\r
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