document.write( "Question 1209639: What are the $x$-coordinate(s) of all point(s) where the parabola $y = f(x)$ intersects the line $y = 0$?\r
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\n" ); document.write( "\n" ); document.write( "f(x) = 2x^2 - 13x + 20 - 5x^2 + 19x + 7.\r
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Algebra.Com's Answer #849717 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "What are the x-coordinate(s) of all point(s) where the parabola y = f(x) intersects the line y = 0?\r
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document.write( "(1)  Simplify  f(x) = 2x^2 - 13x + 20 - 5x^2 + 19x + 7 = -3x^2 + 6x + 27.\r\n" );
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document.write( "(2)  The intersection points of the parabola with the line y = 0\r\n" );
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document.write( "     are the points on x-axis where  -3x^2 + 6x + 27 = 0.\r\n" );
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document.write( "     In Algebra language, these points are called the roots of the equation\r\n" );
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document.write( "          -3x^2 + 6x + 27 = 0.\r\n" );
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document.write( "     In other terminology, these points are called  x-interception points.\r\n" );
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document.write( "(3)  So, your task is to solve this equation\r\n" );
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document.write( "          -3x^2 + 6x + 27 = 0.\r\n" );
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document.write( "     To simplify, divide both side by the common factor -3.  You will get an EQUIVALENT equation\r\n" );
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document.write( "           x^2 - 2x - 9 = 0.\r\n" );
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document.write( "     Apply the quadratic formula\r\n" );
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document.write( "            =  =  = .\r\n" );
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document.write( "(4)  So, the roots of the given equation are  \r\n" );
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document.write( "         =  = -2.162 (rounded)  and  =  = 4.162 (rounded).\r\n" );
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document.write( "     They are x-coordinates of the intersection points.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, with all necessary explanations.\r
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