document.write( "Question 1178755: Use a system of linear equations to find the quadratic function
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\n" ); document.write( "f(1) = 9, f(2) = 10, f(3) = 9 \n" ); document.write( "

Algebra.Com's Answer #808158 by ikleyn(52786) $\"\"$ $\"About$

You can put this solution on YOUR website!
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Let me show you how to solve it without using equations.\n" ); document.write( "
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document.write( "We have a parabola, and its ordinate y at x= 1 is the same as the ordinate y at x= 3.\r\n" );
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document.write( "It means that the parabola's symmetry axis is  x= 2  half way between  x= 1  and x= 3.\r\n" );
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document.write( "Hence, the parabola has a vertex at x= 10, and the vertex form equation is\r\n" );
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document.write( "    y = a*(x-2)^2 + 10.\r\n" );
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document.write( "where \"a\" is a coefficient, now unknown.\r\n" );
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document.write( "To find \"a\", substitute x= 3 into the vertex form equation.\r\n" );
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document.write( "You will get then\r\n" );
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document.write( "    9 = a*(3-2)^2 + 10,   or\r\n" );
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document.write( "    a*1^2 = 9 - 10\r\n" );
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document.write( "       a  = -1.\r\n" );
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document.write( "So, the vertex form equation is\r\n" );
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document.write( "    y = -(x-2)^2 + 10.\r\n" );
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document.write( "Rewrite it in the general form\r\n" );
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document.write( "    y = -(x^2 - 4x + 4) + 10 = -x^2 + 4x + 6.\r\n" );
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document.write( "Thus  a= -1,  b= 4,  c= 6.\r\n" );
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document.write( "                          P L O T\r\n" );
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document.write( "    \r\n" );
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document.write( "              Plot  y =  = \r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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