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What real value of t produces the smallest value of the quadratic t^2 -12t - 36?

 May 23, 2022
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Hint: t^2 - 12t - 36 = (t - 6)^2 - 72. If you want t^2 - 12t - 36 to be the smallest, then you want (t - 6)^2 to be the smallest, but (t - 6)^2 is always >= 0. How can we make (t - 6)^2 = 0, so that the expression t^2 - 12t - 36 is minimized?

 May 23, 2022

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