document.write( "Question 1086039: If the parabola y_1 = x^2 + 2x + 7 and the line y_2 = 6x + b intersect at only one point, what is the value of b? \n" ); document.write( "

Algebra.Com's Answer #700144 by ikleyn(52777) $\"\"$ $\"About$

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\n" ); document.write( "This problem is for Algebra-I, not for Calculus.
\n" ); document.write( "So I will give here another (more adequate) solution.\r
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document.write( "To get the common points, substitute y = 6x + b into the first equation.  You will get\r\n" );
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document.write( "6x + b = .\r\n" );
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document.write( "It is the same as\r\n" );
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document.write( " = 0.   (1)\r\n" );
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document.write( "The original system has a unique solution if and only if the equation (1) has a unique solution.\r\n" );
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document.write( "It happens if and only if the discriminant of the equation (1) is zero:\r\n" );
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document.write( "d =  = 0,   or\r\n" );
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document.write( "16 = 4*(7-b),   or  4 = 7-b,   or   b = 7-4 = 3.\r\n" );
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document.write( "Answer.  b = 3.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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