document.write( "Question 315279: For what value of b will the line y=-2x+b be tangent to the parabola y=3x^2+4x-1 \n" ); document.write( "

Algebra.Com's Answer #225564 by Fombitz(32388) $\"\"$ $\"About$

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The slope of the tangent of the parabola is equal to the value of the derivative.
\n" ); document.write( " $\"y=3x%5E2%2B4x%2B1\"$
\n" ); document.write( " $\"dy%2Fdx=6x%2B4=-2\"$
\n" ); document.write( " $\"6x%2B4=-2\"$
\n" ); document.write( " $\"6x=-6\"$
\n" ); document.write( " $\"x=-1\"$
\n" ); document.write( "So at the point $\"x=-1\"$ , the slope of the tangent line equals -2.
\n" ); document.write( "At that point,
\n" ); document.write( " $\"y=3x%5E2%2B4x%2B1=3-4-1=-2\"$
\n" ); document.write( "So then
\n" ); document.write( " $\"y=-2x%2Bb\"$
\n" ); document.write( " $\"-2=-2%28-1%29%2Bb\"$
\n" ); document.write( " $\"b=-4\"$
\n" ); document.write( "and the equation of the tangent line is,
\n" ); document.write( " $\"y=-2x-4\"$
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