document.write( "Question 82850: when using the quadratic formula to solve a quadratic equation (ax^ + bx + c = 0), the discriminant is b2 - 4ax. This discriminant can be positive, zero, or negative.\r
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Algebra.Com's Answer #59440 by Edwin McCravy(20056) $\"\"$ $\"About$

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when using the quadratic formula to solve a quadratic equation (ax^ + bx + c = 0), the discriminant is b2 - 4ax. This discriminant can be positive, zero, or negative.
\n" ); document.write( "Create three unique equations where the discriminat is positive, zero, or negative. For each case, explain what this value means to the graph of y = ax^ + bx + c.
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document.write( "Case 1.\r\n" );
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document.write( "y = x² + x - 2\r\n" );
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document.write( "a = 1, b = 1, c = -2\r\n" );
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document.write( "Discriminant = b² - 4ac = (1)² - 4(1)(-2) = 1 + 8 = 9\r\n" );
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document.write( "The discriminant 9 is positive so it has two real zeros\r\n" );
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document.write( "Here is the graph:\r\n" );
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document.write( "Its two real zeros are -2 and 1, the x-values at the two \r\n" );
document.write( "points where the graph crosses the x-axis.\r\n" );
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document.write( "Case 2.\r\n" );
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document.write( "y = 4x² - 4x + 1\r\n" );
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document.write( "a = 4, b = -4, c = 1\r\n" );
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document.write( "Discriminant = b² - 4ac = (-4)² - 4(4)(1) = 16 + 16 = 0\r\n" );
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document.write( "The discriminant is zero so it has only one real zero.\r\n" );
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document.write( "Here is the graph:\r\n" );
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document.write( "Its one real zero is at 1/2, the x-value where the graph \r\n" );
document.write( "just touches the x-axis.  We say it is tangent to\r\n" );
document.write( "the x-axis at that one point.\r\n" );
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document.write( "Case 3.\r\n" );
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document.write( "y = x² + x + 1\r\n" );
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document.write( "a = 1, b = 1, c = 1\r\n" );
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document.write( "Discriminant = b² - 4ac = (1)² - 4(1)(1) = 1 - 4 = -3\r\n" );
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document.write( "The discriminant -3 is negative so it has no real zeros.\r\n" );
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document.write( "Here is the graph:\r\n" );
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document.write( "It does not cross or touch the x-axis at all, so there \r\n" );
document.write( "are no real zeros.\r\n" );
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document.write( "Edwin

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