document.write( "Question 1031408: Find the rule of the cubic function that passes through the points (-5,0), (2,0), (3,0) and (0,20). Give your final answer in the form y=ax^3 + bx^2 +cx +d \n" ); document.write( "

Algebra.Com's Answer #646103 by robertb(5830) $\"\"$ $\"About$

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Notice that the points (-5,0), (2,0), (3,0) give the x-intercepts of the cubic function, hence the roots of that function.\r
\n" ); document.write( "\n" ); document.write( "==> $\"f%28x%29+=+k%28x%2B5%29%28x-2%29%28x-3%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "for some undetermined constant k.\r
\n" ); document.write( "\n" ); document.write( "Since f(0) = 20, ==> $\"f%280%29+=+k%280%2B5%29%280-2%29%280-3%29+=+20+\"$ ==> $\"k+=+2%2F3\"$ .\r
\n" ); document.write( "\n" ); document.write( "Therefore the function is $\"f%28x%29+=+%282%2F3%29%28x%2B5%29%28x-2%29%28x-3%29+\"$ , which is just \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29+=+%282%2F3%29x%5E3+-+%2838%2F3%29x+%2B+20\"$ . \n" ); document.write( "

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