document.write( "Question 121168: What function represents the data in the following tables?
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Algebra.Com's Answer #89059 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "a) x-   0 | 1 | 2 | 3\r\n" );
document.write( "   y-  24 |12 | 6 | 3\r\n" );
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document.write( "That means it contains the 4 points \r\n" );
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document.write( "(0,24), (1,12), (2,6) and (3,3)\r\n" );
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document.write( "The polynomial of least degree which has 4 \r\n" );
document.write( "coefficients is a third degree (cubic) polynomial:\r\n" );
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document.write( "y = ax³ + bx² + cx + d\r\n" );
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document.write( "Subnstitute each of those points in:\r\n" );
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document.write( "24 = a(0)³ + b(0)² + c(0) + d\r\n" );
document.write( "24 = d\r\n" );
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document.write( "12 = a(1)³ + b(1)² + c(1) + d\r\n" );
document.write( "12 = a + b + c + d\r\n" );
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document.write( "6 = a(2)³ + b(2)² + c(2) + d\r\n" );
document.write( "6 = 8a + 4b + 2c + d\r\n" );
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document.write( "3 = a(3)³ + b(3)² + c(3) + d\r\n" );
document.write( "3 = 27a + 9b + 3c + d\r\n" );
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document.write( "So you have the system of 4 equations \r\n" );
document.write( "in 4 unknowns:\r\n" );
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document.write( "24 = d\r\n" );
document.write( "12 = a + b + c + d\r\n" );
document.write( "6 = 8a + 4b + 2c + d \r\n" );
document.write( "3 = 27a + 9b + 3c + d\r\n" );
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document.write( "Can you solve that? If not post again.\r\n" );
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document.write( "a = -1/2, b = 9/2, c = -16, d = 24.\r\n" );
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document.write( "So the formula\r\n" );
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document.write( "y = ax³ + bx² + cx + d\r\n" );
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document.write( "becomes\r\n" );
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document.write( "y = x³ + x² - 16x + 24\r\n" );
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document.write( "or letting y = f(x)\r\n" );
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document.write( "f(x) = x³ + x² - 16x + 24\r\n" );
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document.write( "This is done the exact same way:\r\n" );
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document.write( "b) x-   0 | 3 | 6 | 9\r\n" );
document.write( "   y-   5 |10 |20 |40\r\n" );
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document.write( "That means it contains the 4 points \r\n" );
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document.write( "(0,5), (3,10), (6,20) and (9,40)\r\n" );
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document.write( "The polynomial of least degree which has 4 \r\n" );
document.write( "coefficients is a third degree (cubic) polynomial:\r\n" );
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document.write( "y = ax³ + bx² + cx + d\r\n" );
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document.write( "Substitute each of those points in:\r\n" );
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document.write( "5 = a(0)³ + b(0)² + c(0) + d\r\n" );
document.write( "5 = d\r\n" );
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document.write( "10 = a(3)³ + b(3)² + c(3) + d\r\n" );
document.write( "10 = 27a + 9b + 3c + d\r\n" );
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document.write( "20 = a(6)³ + b(6)² + c(6) + d\r\n" );
document.write( "20 = 216a + 36b + 6c + d\r\n" );
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document.write( "40 = a(9)³ + b(9)² + c(9) + d\r\n" );
document.write( "40 = 729a + 81b + 9c + d\r\n" );
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document.write( "So you have the system of 4 equations \r\n" );
document.write( "in 4 unknowns:\r\n" );
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document.write( " 5 = d\r\n" );
document.write( "10 = 27a + 9b + 3c + d\r\n" );
document.write( "20 = 216a + 36b + 6c + d\r\n" );
document.write( "40 = 729a + 81b + 9c + d\r\n" );
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document.write( "Can you solve that? If not post again.\r\n" );
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document.write( "a = 5/162, b = 0, c = 25/18, d = 5.\r\n" );
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document.write( "So the formula\r\n" );
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document.write( "y = ax³ + bx² + cx + d\r\n" );
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document.write( "becomes\r\n" );
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document.write( "y = x³ + 0x² - x + 5\r\n" );
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document.write( "or letting y = f(x)\r\n" );
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document.write( "f(x) = x³ - x + 5\r\n" );
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document.write( "Edwin

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