document.write( "Question 252969: For what positive value of k is the graph of y = kx^2 + 6x + k +8 tangent to the x axis? \n" ); document.write( "

Algebra.Com's Answer #185161 by drk(1908) $\"\"$ $\"About$

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We want to apply the following equation:
\n" ); document.write( "lim(h->0) $\"%28f%28x%2Bh%29-f%28x%29%29%2Fh\"$
\n" ); document.write( "f(x+h) = k(x+h)^2 -6k + k
\n" ); document.write( "F(x+h) - f(x) = 2kxh + kh^2 + 6h
\n" ); document.write( "(F(x+h) - f(x))/h = 2xk + kh + 6
\n" ); document.write( "lim(h->0)F(x+h) - f(x) = 2xk + 6.
\n" ); document.write( "SInce we want tangent to the x-axis, y = 0. So,
\n" ); document.write( "K = -6/2x = -3/x.
\n" ); document.write( "We want positive values of k, so x = -1, or x = -3.
\n" ); document.write( "If x = -1, then k = 3 and
\n" ); document.write( "f(x) = 3x^2 + 6x + 3
\n" ); document.write( "f(x) = 3(x^2 + 2x + 1)
\n" ); document.write( "f(x) = 3(x+1)^2.
\n" ); document.write( "If x = -3, then k = 1, however this doesn't meet our criteria. \n" ); document.write( "

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