What value of y within the range of −3 to 3, inclusive, maximizes the expression $y^2 − 8y + 12$ ?

Correct answer marked below

−3

Correct

−1

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Explanation

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Official Explanation

Official

To determine the value of y that maximizes the expression

y^2 − 8y + 12

, we note that the term

y^2

is always non-negative, while the term

-8y

becomes positive when

y

is negative.

Thus, the expression achieves its maximum when y is at its lowest value within the specified range.…

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What this question tests

Your ability to manipulate linear and quadratic expressions, substitute unknowns, and solve equations under time pressure.

Losing a sign when moving terms across the equals sign, or dividing both sides by a variable that could equal zero.