document.write( "Question 1187461: find the equation of the parabola determined by the given condition: axis vertical and passing through (0,0), (1,0), and (5,-20) \n" ); document.write( "

Algebra.Com's Answer #818448 by ikleyn(52798) $\"\"$ $\"About$

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\n" ); document.write( "find the equation of the parabola determined by the given condition:
\n" ); document.write( "axis vertical and passing through (0,0), (1,0), and (5,-20).
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document.write( "From the condition, you see that the quadratic polynomial has zeroes at x= 0 and x= 1.\r\n" );
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document.write( "It means that the quadratic polynomial has this factored form\r\n" );
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document.write( "    y(x) = ax*(x-1),\r\n" );
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document.write( "where \"a\" is an unknown coefficient.\r\n" );
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document.write( "To find this coefficient, use the third point, which says that  y(5) = -20\r\n" );
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document.write( "    a*5*(5-1) = -20,\r\n" );
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document.write( "or\r\n" );
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document.write( "    20a = -20,\r\n" );
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document.write( "which gives  a = -20/20 = -1.\r\n" );
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document.write( "So, the sough function (polynomial) is  y(x) = -x*(x-1) = -x^2 + x.    ANSWER\r\n" );
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