Question 524256: determine the set of values of k for which the line 2y=x+k does not intersect the curve y=x^2-4x+7
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! determine the set of values of k for which the line 2y=x+k does not intersect the curve y=x^2-4x+7
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Since the quadratic opens up you cannot get above it for all values of "x".
So go below it.
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The minimum of the quadratic occurs when x = -b/(2a) = 4/2 = 2
f(2) = 4-8+7 = 3
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Minimum at (2,3)
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Find the line equation where 2y=x+k passing thru (2,3)
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2*3 = 2+k
k = 4
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Equation:
2y= x+4
y = (1/2)x+2
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Answer: k < 4
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Cheers,
Stan H.
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