document.write( "Question 1108425: Show that the line y=4x+17 is a tangent to the parabola with equation y=8-2x-x^2 \n" ); document.write( "

Algebra.Com's Answer #723437 by ikleyn(52858) $\"\"$ $\"About$

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document.write( "First we need to find common points to the parabola and the straight line.\r\n" );
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document.write( "For it, from the given equations, you have\r\n" );
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document.write( "4x + 17 = 8 - 2x - x^2,     (since left sides of the given equations are identical, their RIGHT sides are equal !)\r\n" );
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document.write( "Then \r\n" );
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document.write( "x^2 + 6x + 9 = 0.\r\n" );
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document.write( "It is the same as\r\n" );
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document.write( "(x+3)^2 = 0,\r\n" );
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document.write( "and this equation has ONLY ONE real root x= -3.\r\n" );
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document.write( "It means that the straight line and the parabola have ONLY ONE COMMON POINT.\r\n" );
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document.write( "In turn, it means that the given straight line is TANGENT to the parabola..\r\n" );
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document.write( "Thus the STATEMENT in your post is PROVED.\r\n" );
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document.write( "Plots y = 4x+17 (red)  and  y =  (green)\r\n" );
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