document.write( "Question 1181254: Given points A(0, 1), B(2, 5) and point P moving along the parabola y = x^2 + 4x + 7 …eq. 1, find the minimum value of area S of triangle PAB \n" ); document.write( "

Algebra.Com's Answer #811118 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "Let P(x,y) be an arbitrary point along the parabola.\r\n" );
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document.write( "Use the distance formula to find \r\n" );
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document.write( "Use the slope formula and the point-slope formula to find the\r\n" );
document.write( "equation of AB which is \r\n" );
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document.write( "Use the perpendicular distance from point to line formula to find PQ, \r\n" );
document.write( "which is:\r\n" );
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document.write( "d =  = distance from point (x₁, y₁) to line Ax+By+C=0\r\n" );
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document.write( "So we find the minimum value of  by using the\r\n" );
document.write( "vertex formula.  The vertex formula for the x-coordinate of the\r\n" );
document.write( "vertex of parabola  is .\r\n" );
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document.write( "So the x-coordinate of the parabola  is \r\n" );
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document.write( "The minimum value is the y-coordinate of the vertex, which is\r\n" );
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document.write( "So the minimum area S of triangle PAB is S = 5\r\n" );
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document.write( "The original drawing should look like this:\r\n" );
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document.write( "Edwin

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