document.write( "Question 914680: Determine the value of k such that g(x)= 3x + k intersects the quadratic function f(x)=2x^2-5x+3 at exactly one point. \n" ); document.write( "

Algebra.Com's Answer #555531 by Fombitz(32388) $\"\"$ $\"About$

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At only 1 point means the line is tangent to the curve.
\n" ); document.write( "Since the slope of the line is fixed, find when the slope of the tangent line to the curve has a slope of $\"m=3\"$ .
\n" ); document.write( "The slope of the tangent line is the value of the derivative.
\n" ); document.write( " $\"df%2Fdx=4x-5\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"4x-5=3\"$
\n" ); document.write( " $\"4x=8\"$
\n" ); document.write( " $\"x=2\"$
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\n" ); document.write( "Find the y-coordinate now.
\n" ); document.write( "When $\"x=2\"$ , $\"f%282%29=2%284%29-5%282%29%2B3\"$
\n" ); document.write( " $\"f%282%29=8-10%2B3\"$
\n" ); document.write( " $\"f%282%29=1\"$
\n" ); document.write( "The line must have the same y-coordinate, so,
\n" ); document.write( " $\"g%282%29=3%282%29%2Bk=1\"$
\n" ); document.write( " $\"6%2Bk=1\"$
\n" ); document.write( " $\"k=-5\"$
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