SOLUTION: Find k so that the minimum value of f(x) =x^2 +kx+8 is equal to the maximum value of g(x) = 1 +4x-2x^2.

Question 1017094: Find k so that the minimum value of f(x) =x^2 +kx+8 is equal to the maximum value of g(x) = 1 +4x-2x^2.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find k so that the minimum value of f(x) =x^2 +kx+8 is equal to the maximum value of g(x) = 1 +4x-2x^2.
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Note:: Max or Min occurs at -b(2a)
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min of f(x) at (-k/2,f(-k/2))
max of g(x) at (-4/-4,g(1))
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Solve::
f(-k/2) = g(1)
(-k/2)^2 + k(-k/2) + 8 = 1 + 4 - 2
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k^2/4 - k^2/2 + 5 = 0
k^2 - 2k^2 + 20 = 0
k^2 = 20
k = 2sqrt(5)
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Cheers,
Stan H.
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