document.write( "Question 702329: Find an expression for a cubic function f if f(5) = 300 and f(-5) = f(0) = f(6) = 0. \n" ); document.write( "
Algebra.Com's Answer #432908 by Edwin McCravy(20065)\"\" \"About 
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Find an expression for a cubic function f if f(5) = 300 and f(-5) = f(0) = f(6) = 0.
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document.write( "Start with the general cubic:\r\n" );
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document.write( "f(x) = A·x³ + B·x² + C·x + D\r\n" );
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document.write( "Use f(5) = 300 and f(-5) = f(0) = f(6) = 0 to form four equations:\r\n" );
document.write( "f(5) = A·(5)³ + B·(5)² + C·(5) + D = 300\r\n" );
document.write( "f(-5) = A·(-5)³ + B·(-5)² + C·(-5) + D = 0\r\n" );
document.write( "f(0) = A·(0)³ + B·(0)² + C·(0) + D = 0\r\n" );
document.write( "f(6) = A·(6)³ + B·(6)² + C·(6) + D = 0\r\n" );
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document.write( "We simplify them to this system of four equations in four unknowns\r\n" );
document.write( " 125A + 25B + 5C + D = 300\r\n" );
document.write( "-125A + 25B - 5C + D =   0\r\n" );
document.write( "                   D =   0\r\n" );
document.write( " 216A + 36B + 6C + D =   0\r\n" );
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document.write( "And since the third equation tells us that D=0 we can simplify the \r\n" );
document.write( "other equations and just have three equations in three unknowns:\r\n" );
document.write( " 125A + 25B + 5C = 300\r\n" );
document.write( "-125A + 25B - 5C =   0\r\n" );
document.write( " 216A + 36B + 6C =   0\r\n" );
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document.write( "That's pretty easy to solve.\r\n" );
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document.write( "A=-6, B=6, C=180, and we already had D=0\r\n" );
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document.write( "So  \r\n" );
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document.write( "f(x) = A·x³ + B·x² + C·x + D\r\n" );
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document.write( "becomes:\r\n" );
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document.write( "f(x) = -6x³ + 6x² + 180x\r\n" );
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document.write( "Edwin
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