document.write( "Question 578107: Hello, i have been given this maths question, please could you help me solve it. I have tried putting it into a quadratic equation then i realised that it cannot be factorised. The question is:\r
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Algebra.Com's Answer #370562 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
prove that the line y+x=-2 is a tangent to the curve y^2 = 8x.
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document.write( "A line which intersects a parabola exactly once and which is not \r\n" );
document.write( "parallel to the axis of symmetry, is tangent to the parabola.  \r\n" );
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document.write( "y + x = -2 is a tangent to the curve y² = 8x\r\n" );
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document.write( "The axis of symmetry of that parabola is the \r\n" );
document.write( "x-axis, and the line y + x = -2 is not parallel\r\n" );
document.write( "to the x-axis, so if it intersects the parabola\r\n" );
document.write( "exactly once, then it is tangent to the parabola.\r\n" );
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document.write( "We solve the equation of the line for y\r\n" );
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document.write( "    y + x = -2 - x\r\n" );
document.write( "        y = -2 - x\r\n" );
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document.write( "And we substitute (-2 - x) for y in\r\n" );
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document.write( "            y² = 8x\r\n" );
document.write( "     (-2 - x)² = 8x\r\n" );
document.write( "   4 + 4x + x² = 8x \r\n" );
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document.write( "   x² - 4x + 4 = 0\r\n" );
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document.write( "(x - 2)(x - 2) = 0\r\n" );
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document.write( "x - 2 = 0,  x - 2 = 0\r\n" );
document.write( "    x = 2       x = 2\r\n" );
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document.write( "Th fact that -2 is a double root for x shows that \r\n" );
document.write( "there is just one point of intersection and so the\r\n" );
document.write( "line is tangent to the parabola at the point were\r\n" );
document.write( "x = 2, which has y-coordinate y = -2 - (2) = -4\r\n" );
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document.write( "or the point (2,-4) is the point of tangency.\r\n" );
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document.write( "Edwin
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