document.write( "Question 160346: hey,
\n" ); document.write( "could you please solve the following question, thanks,
\n" ); document.write( "The graph of function y= x^2 - kx + k + 8 touches the x-axis at one point. What
\n" ); document.write( "is the value of k?\r
\n" ); document.write( "\n" ); document.write( "I will be waiting for the solution,
\n" ); document.write( "and thanks again,
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Algebra.Com's Answer #118307 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
The graph of function y= x^2 - kx + k + 8 touches the x-axis at one point. What
\n" ); document.write( "is the value of k?
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\n" ); document.write( "we use the discriminant: b^2 - 4*a*c = 0; when it touches one point on the x axis (a double root)
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\n" ); document.write( "in this equation a=1, b=k, c=(k+8)
\n" ); document.write( "Substitute:
\n" ); document.write( "k^2 - 4*1*(k+8) = 0
\n" ); document.write( "k^2 - 4k - 32 = 0
\n" ); document.write( "Factor
\n" ); document.write( "(k-8)(k+4) = 0
\n" ); document.write( "Two solutions
\n" ); document.write( "k = 8
\n" ); document.write( "k = -4
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\n" ); document.write( "for k=8
\n" ); document.write( "x^2 - 8x + 8 + 8 = 0
\n" ); document.write( "x^2 - 8x + 16 = 0; which is(x-4)^2 a double root at x=4
\n" ); document.write( "and for k=-4
\n" ); document.write( "x^2 -(-4)x + (-4) + 8 = 0
\n" ); document.write( "x^2 + 4x + 4 = 0; which is(x+2)^2 a double root at x=-2
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\n" ); document.write( "Did that help? \n" ); document.write( "
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