document.write( "Question 420624: If possible, sketch a graph of a polynomial that satisfies the conditions. Let a be the leading coefficient.\r
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Algebra.Com's Answer #293869 by Edwin McCravy(20055)\"\" \"About 
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document.write( "1. It is IMPOSSIBLE to have a polynomial of ODD degree \r\n" );
document.write( "greater than 1 which is symmetrical with respect to the \r\n" );
document.write( "Y-AXIS.  \r\n" );
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document.write( "So the answer to your question is \"It is impossible\". \r\n" );
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document.write( "2. It is POSSIBLE to have a polynomial of EVEN degree \r\n" );
document.write( "which is symmetrical with respect to the Y-AXIS.\r\n" );
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document.write( "3. It is POSSIBLE to have a polynomial of ODD degree \r\n" );
document.write( "greater than 1 which is symmetrical with respect to the \r\n" );
document.write( "ORIGIN.  \r\n" );
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document.write( "4. It is IMPOSSIBLE to have a polynomial of EVEN degree \r\n" );
document.write( "which is symmetrical with respect to the ORIGIN.\r\n" );
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document.write( "The reason for the above is given by the extreme right \r\n" );
document.write( "and left hand behavior rules, which are given below:\r\n" );
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document.write( "Leading Coefficient Test (right hand behavior)\r\n" );
document.write( "•If the leading coefficient, an, of the polynomial is \r\n" );
document.write( "positive, then the right hand side of the graph will \r\n" );
document.write( "rise towards + infinity. \r\n" );
document.write( "•If the leading coefficient, an, of the polynomial is \r\n" );
document.write( "negative, then the right hand side of the graph will fall\r\n" );
document.write( "towards - infinity.\r\n" );
document.write( "Degree of the Polynomial (left hand behavior)\r\n" );
document.write( "•If the degree, n, of the polynomial is even, the left hand side \r\n" );
document.write( "will do the same as the right hand side.\r\n" );
document.write( "•If the degree, n, of the polynomial is odd, the left hand side \r\n" );
document.write( "will do the opposite of the right hand side.\r\n" );
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document.write( "In order to be symmetrical with respect to the y-axis, a \r\n" );
document.write( "polynomial must do the same on both extreme sides, so its degree\r\n" );
document.write( "must be even.\r\n" );
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document.write( "In order to be symmetrical with the origin, a polynomial must do\r\n" );
document.write( "the opposite on both extreme sides, so its degree must be odd.\r\n" );
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document.write( "Edwin

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