document.write( "Question 1193921: The graph of the quadratic function y = (3k - 1)(x^2) - 6x +1 where k € R, has a positive concavity and passes through the x-axis twice. Find the range of possible values for k. \n" ); document.write( "
Algebra.Com's Answer #825967 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"y+=+%283k-1%29+x%5E2+-+6+x+%2B+1\"\r\n" );
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document.write( "has positive concavity when its graph, a parabola, opens upward, \r\n" );
document.write( "which is when the coefficient of x2 is positive, which means \r\n" );
document.write( "greater than 0, so solve the inequality for k:\r\n" );
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document.write( "\"3k-1%3E0\"\r\n" );
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document.write( "Also to pass through the x-axis twice, its discriminant must \r\n" );
document.write( "be positive to give it two unique real zeros.  So simplify \r\n" );
document.write( "and solve this inequality for k:\r\n" );
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document.write( "\"b%5E2-4ac%3E0\"\r\n" );
document.write( "\"%28-6%29%5E2-4%283k-1%29%281%29%3E0\"\r\n" );
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document.write( "Now look at the two solutions to those two inequalities and \r\n" );
document.write( "fill in fractions in the two blanks. \r\n" );
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document.write( "___ < k < ___\r\n" );
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document.write( "Edwin
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