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secondary 3 | A Maths
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Date Posted: 4 years ago
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4x - x^2 - 7
= -x^2 + 4x -7
=-(x^2 -4x) -7
= -(x^2 -4x) -4 + 4 -7
=-(x^2 -4x +4) +4 - 7
=-(x+2) ^2 -3
Since -(x+2)^2 is smaller or equal to 0, -(x+2) ^2 -3 will be smaller or equal to -3. Thus, 4x - x^2 - 7 is always negative.
= -x^2 + 4x -7
=-(x^2 -4x) -7
= -(x^2 -4x) -4 + 4 -7
=-(x^2 -4x +4) +4 - 7
=-(x+2) ^2 -3
Since -(x+2)^2 is smaller or equal to 0, -(x+2) ^2 -3 will be smaller or equal to -3. Thus, 4x - x^2 - 7 is always negative.
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