document.write( "Question 1014924: Given the quadratic function y=x^2-x+k-1 and the linear function y=x+1, find the number of points that their graphs have in common. (assume k>4) \n" ); document.write( "

Algebra.Com's Answer #631237 by robertb(5830) $\"\"$ $\"About$

You can put this solution on YOUR website!
Solve the system of equations $\"y+=+x%5E2+-x+%2Bk+-+1\"$ and y = x + 1.\r
\n" ); document.write( "\n" ); document.write( "Then $\"x%5E2+-x+%2Bk+-+1+=+x+%2B1\"$ , or $\"x%5E2+-2x+%2Bk+-+2=0\"$ .\r
\n" ); document.write( "\n" ); document.write( "The discriminant is then equal to $\"b%5E2+-+4ac+=+4+-+4%281%29%28k-2%29+=+12+-+4k\"$ .\r
\n" ); document.write( "\n" ); document.write( "Since it is given that k > 4, it follows that:\r
\n" ); document.write( "\n" ); document.write( "-4k < -16,
\n" ); document.write( "12 - 4k < 12 - 16 = -4,
\n" ); document.write( "12 - 4k < -4 < 0,
\n" ); document.write( "hence the discriminant is negative, and thus the system has no (real) solutions. Therefore the two graphs don't have points in common. (They do not intersect.)\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );