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Advanced MathHardMinimum value from vertex form with a coefficient

Advanced Math practice question

The function d is defined by d(x) = 2(x + 1)² − 8. Which statement is true?

  1. A. Its minimum value is −8, at x = −1.Correct
  2. B. Its minimum value is −8, at x = 1.
  3. C. Its maximum value is −8, at x = −1.
  4. D. Its minimum value is −1, at x = −8.

Answer: A. Its minimum value is −8, at x = −1.

2(x + 1)² ≥ 0 with equality at x = −1, so the minimum is −8 there.

Why the other answers are wrong

B. Its minimum value is −8, at x = 1.
(x + 1)² is zero at x = −1, not 1.
C. Its maximum value is −8, at x = −1.
The coefficient 2 is positive: the parabola opens upward, so −8 is a minimum.
D. Its minimum value is −1, at x = −8.
Swaps the vertex's coordinates.

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