Advanced Math practice question

Answer: 25

f(x) = (x − 5)² + (c − 25). It stays nonnegative exactly when c − 25 ≥ 0, so the smallest c is 25.

Common wrong answers

If you answered 5

5 is half the coefficient; the required constant is its square, 25.

If you answered 10

10 is the x-coefficient's magnitude; completing the square needs (10/2)² = 25.

If you answered 100

100 is 10²; the completed square uses (10/2)² = 25.

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