document.write( "Question 76424: Can you help me with this please?? \r
\n" ); document.write( "\n" ); document.write( "When using the quadratic formula to solve a quadratic equation ax2 + bx + c = 0, the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. (When the discriminant is negative, then we have the square root of a negative number. This is called an imaginary number, sqrt(-1) = i. )\r
\n" ); document.write( "\n" ); document.write( "Explain what the value of the discriminant means to the graph of y = ax2 + bx + c. Hint: Chose values of a, b and c to create a particular discriminant. Then, graph the corresponding equation.
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Algebra.Com's Answer #54812 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "When using the quadratic formula to solve a quadratic \r\n" );
document.write( "equation , the discriminant is \r\n" );
document.write( ". This discriminant can be positive, \r\n" );
document.write( "zero, or negative. (When the discriminant is negative, \r\n" );
document.write( "then we have the square root of a negative number. \r\n" );
document.write( "This is called an imaginary number, sqrt(-1) = i. )\r\n" );
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document.write( "Explain what the value of the discriminant means to \r\n" );
document.write( "the graph of y = ax2 + bx + c. Hint: Chose values of \r\n" );
document.write( "a, b and c to create a particular discriminant.  Then, \r\n" );
document.write( "graph the corresponding equation?\r\n" );
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document.write( "Choose a = 1, b = 4, c = -21\r\n" );
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document.write( "Then the equation is y = x² + 4x - 21 and the \r\n" );
document.write( "discriminant is\r\n" );
document.write( "(4)² - 4(1)(-21) = 16 + 84 = 100, which is positive.  \r\n" );
document.write( "The graph intersects the x-axis twice, once at \r\n" );
document.write( "x = -7 and again at x = 3. There are two real \r\n" );
document.write( "zeros, -7, and 3\r\n" );
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document.write( "Now choose a = 1, b = 4, c = 4\r\n" );
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document.write( "Then the equation is y = x² + 4x + 4 and the \r\n" );
document.write( "discriminant is (4)² - 4(1)(4) = 16 - 16 = 0.  \r\n" );
document.write( "The graph just touches the x-axis at -2.  \r\n" );
document.write( "There is just one real zeros, -2.  [This zero \r\n" );
document.write( "is said to have multiplicity 2 because people \r\n" );
document.write( "like to think of the graph as \"crossing the \r\n" );
document.write( "x-axis twice at the same point\", and \"both its \r\n" );
document.write( "two zeros are the same, i.e., 'merging' into\r\n" );
document.write( "one\".]\r\n" );
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document.write( "Finally choose a = 1, b = 4, c = 6\r\n" );
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document.write( "Then the equation is y = x² + 4x + 6 and the \r\n" );
document.write( "discriminant is (4)² - 4(1)(6) = 16 - 24 = -8, \r\n" );
document.write( "which is negative.  The graph does not cross \r\n" );
document.write( "or touch the x-axis.  Therefore it has no real\r\n" );
document.write( "zeros, which means that both its solutions are \r\n" );
document.write( "imaginary.\r\n" );
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document.write( "Edwin

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