document.write( "Question 1153918: The graph of a parabola passes through the points (3/2, 4/3) and (0, −6) and
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Algebra.Com's Answer #776243 by ikleyn(52800) $\"\"$ $\"About$

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document.write( "Since the parabola has a horizontal tangent line at the point (3/2,4/3), it means \r\n" );
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document.write( "that this point (3/2,4/3) is the vertex of the parabola.\r\n" );
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document.write( "Hence, the parabola has the form\r\n" );
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document.write( "    y(x) = ,\r\n" );
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document.write( "where \"a\" is a coefficient (real number), now unknown.\r\n" );
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document.write( "To find \"a\", use the fact that the plot of the parabola passes through the point (0,-6). It means that\r\n" );
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document.write( "    y(0) = -6,   or    = -6,   or\r\n" );
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document.write( "     = -6.\r\n" );
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document.write( "It gives\r\n" );
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document.write( "     =  =  = ,\r\n" );
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document.write( "hence\r\n" );
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document.write( "    a =  = .\r\n" );
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document.write( "Thus the equation of the parabola is  \r\n" );
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document.write( "    y(x) = .\r\n" );
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document.write( "You can transform it to any other equivalent form you wish.\r\n" );
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document.write( "Regarding the plot, do it on your own.\r\n" );
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document.write( "You may use free of charge plotting tools from the Internet.\r\n" );
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