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?
- A. Its minimum value is −8, at x = −1.Correct
- B. Its minimum value is −8, at x = 1.
- C. Its maximum value is −8, at x = −1.
- 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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