document.write( "Question 195272: Without drawing the graph of the equation, determine how many points the parabola has in common with the x-axis and whether its vertex lies above, on, or below the x-axis. y = 3x2 - 12x + 12
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Algebra.Com's Answer #146463 by Edwin McCravy(20056) $\"\"$ $\"About$

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Without drawing the graph of the equation, determine how many points the parabola has in common with the x-axis and whether its vertex lies above, on, or below the x-axis. \r
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document.write( "Rules for :\r\n" );
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document.write( "If a is positive the parabola opens upward.\r\n" );
document.write( "If a is negative the parabola opens downward.\r\n" );
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document.write( "Calculate d, the discriminant where the\r\n" );
document.write( "discriminant is given by \r\n" );
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document.write( "If d is positive the parabola has exactly 2 points\r\n" );
document.write( "in common with the x-axis.\r\n" );
document.write( "If d is negative the parabola has NO points in\r\n" );
document.write( "common with the x-axis.\r\n" );
document.write( "Id d is zero the parabola has exactly 1 point in\r\n" );
document.write( "common with the x-axis, and that one point is the \r\n" );
document.write( "vertex of the parabola.\r\n" );
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document.write( "Then calculate a*d\r\n" );
document.write( "If a*d is positive, the vertex is below the x-axis\r\n" );
document.write( "If a*d is negative, the vertex is above the x-axis \r\n" );
document.write( "If a*d is zero, the vertex is on the x-axis\r\n" );
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document.write( "In your problem a=3, b=-12, c=12, so\r\n" );
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document.write( "Since a=3 is positive the parabola opens upward.\r\n" );
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document.write( "We calculate d:\r\n" );
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document.write( "So the discriminant is 0, and ad = 0, so the vertex\r\n" );
document.write( "is on the x-axis and has only that one point in\r\n" );
document.write( "common with the x-axis.\r\n" );
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document.write( "Now that we have done it without the graph, we can\r\n" );
document.write( "check by drawing the graph:\r\n" );
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document.write( "Edwin

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