Question 160346
The graph of function y= x^2 - kx + k + 8 touches the x-axis at one point. What
is the value of k? 
:
we use the discriminant: b^2 - 4*a*c = 0; when it touches one point on the x axis (a double root)
:
in this equation a=1, b=k, c=(k+8)
Substitute:
k^2 - 4*1*(k+8) = 0
k^2 - 4k - 32 = 0
Factor
(k-8)(k+4) = 0
Two solutions
k = 8
k = -4
:
for k=8
x^2 - 8x + 8 + 8 = 0
x^2 - 8x + 16 = 0; which is(x-4)^2 a double root at x=4
and for k=-4
x^2 -(-4)x + (-4) + 8 = 0
x^2 + 4x + 4 = 0; which is(x+2)^2 a double root at x=-2
:
{{{ graph( 300, 200, -10, 10, -10, 10, x^2-8x+16, x^2+4x+4) }}}
:
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