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In an equation of the form $k = ax^2 + bx + c$ with $a > 0$, the least possible value of $k$ occurs at $x = -b/(2a)$. In the equation $k = (6x + 12)(x - 8)$, what is the least possible value for $k$?

 

Thank you in advance, and sorry if this question was already posted before. 

 May 16, 2022
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Expand (6x + 12)(x - 8), we get 6x^2 - 36x - 96.  Therefore, k = -b/(2a) = -(-36)/(2*6) = 3.

 May 16, 2022

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