document.write( "Question 1209656: What is the smallest distance between the origin and a point on the graph of y = \frac{1}{\sqrt{3}} (x^2 - 7 + 2x)? \n" ); document.write( "

Algebra.Com's Answer #851866 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "What is the smallest distance between the origin and a point on the graph of y = $\"%281%2Fsqrt%283%29%29%2A%28x%5E2+-+7+%2B+2x%29\"$ ?
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document.write( "The square of the distance from the origin to the point (x,y) is  D = x^2 + y^2.\r\n" );
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document.write( "We have \r\n" );
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document.write( "    D = x^2 + y^2 = x^2 + \r\n" );
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document.write( "I will not simplify this expression.\r\n" );
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document.write( "Instead, I will find the minimum of D over {x} graphically.\r\n" );
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document.write( "I use the plotting tool at website  www.desmos.com/calculator/\r\n" );
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document.write( "It provides the plot (free of charge) and the position and the coordinates of the minimum.\r\n" );
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document.write( "My plot is under this link https://www.desmos.com/calculator/4phmfmwfj7\r\n" );
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document.write( "To see the coordinates of the minimum, click on it.\r\n" );
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document.write( "We have   = 3.04039  approximately.\r\n" );
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document.write( "Hence, the minimum distance under the problem's question is   = 1.7437.\r\n" );
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document.write( "ANSWER.  The smallest distance between the origin and a point on the graph \r\n" );
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document.write( "         of  y =   is  1.7437, approximately.\r\n" );
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