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Complete the square to determine the minimum or maximum value of the function defined by the expression -x^2-4x+15

Complete the square to determine the minimum or maximum value of the function defined by the expression -x^2-4x+15
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complete the square to determine the minimum or maximum value of the function defined by the expression -x^2-4x+15

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User Upgradingdave
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- {x}^(2) - 4x + 15 \\ = - {x}^(2) - 4x - 4 + 15 + 4 \\ = - ( {x}^(2) + 4x + 4) + 19 \\ = \underbrace{- {(x + 2)}^(2)}_( \leqslant 0) + 19 \\ \Rightarrow - {(x + 2)}^(2) + 19 \leqslant 19 \\ \Rightarrow Maximum \: value \: is \: 19 \: as \: x=-2</p><p>

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User Gks
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