document.write( "Question 1179834: The graph of a quadratic function passes through the origin and has
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\n" ); document.write( "\n" ); document.write( "Use symmetry to identify one other point that must be on the graph of
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Algebra.Com's Answer #809423 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "The graph of a quadratic function passes through the origin and has
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\n" ); document.write( "\n" ); document.write( "Use symmetry to identify one other point that must be on the graph of
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\n" ); document.write( "\n" ); document.write( "Find an equation for this function.
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document.write( "The other point is the point symmetrical to the origin point (0,0) relative to the axis of symmetry x=4 of the parabola.\r\n" );
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document.write( "This symmetrical point is 4 units to the right relative the symmetry line x=4,\r\n" );
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document.write( "and it has the same y-coordinate of 0.\r\n" );
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document.write( "So, the other point is (8,0).\r\n" );
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document.write( "The equation of the parabola in the vertex form is\r\n" );
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document.write( "    y = \"a%2A%28x-4%29\" + 16.     (1)\r\n" );
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document.write( "Since it is going through the origin point  (x,y) = (0,0),  from equation (1) we have\r\n" );
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document.write( "    0 = \"a%2A%280-4%29%5E2\" + 16,   or\r\n" );
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document.write( "    0 = 16a + 16\r\n" );
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document.write( "    16a = -16,\r\n" );
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document.write( "      a = \"-16%2F16\" = -1.\r\n" );
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document.write( "Thus the equation of the parabola is  \r\n" );
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document.write( "      y = \"-%28x-4%29%5E2+%2B+16\".\r\n" );
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document.write( "    \r\n" );
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document.write( "    Plot y = \"-%28x-4%29%5E2%2B16\".\r\n" );
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\n" ); document.write( "\n" ); document.write( "Comparing my solution with that by @MathLover1,  notice  the difference:\r
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\n" ); document.write( "\n" ); document.write( "            the problem asks to find the point on the plot,  symmetric to the origin of coordinates.\r
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\n" ); document.write( "\n" ); document.write( "            The origin of coordinates is the point  (0,0),  and the point symmetrical to it is the point  (8,0),  as  I  responded.\r
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\n" ); document.write( "\n" ); document.write( "            @MathLover1 considers totally different points,  that are  IRRELEVANT  to the posed question.\r
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