Advanced MathHardMaximum and zeros from vertex form
Advanced Math practice question
The function u is defined by u(x) = −2(x + 1)² + 8. Which statement is true?
- A. u has a maximum value of 8, and u(x) = 0 at x = 1 and x = −3.Correct
- B. u has a minimum value of 8.
- C. u has a maximum value of 8, and u(x) = 0 at x = 3 and x = −1.
- D. u has a maximum value of −2.
Answer: A. u has a maximum value of 8, and u(x) = 0 at x = 1 and x = −3.
The leading coefficient is negative, so 8 is the maximum (at x = −1). Zeros: (x + 1)² = 4, x = 1 or −3.
Why the other answers are wrong
- B. u has a minimum value of 8.
- A negative coefficient gives a maximum, not a minimum.
- C. u has a maximum value of 8, and u(x) = 0 at x = 3 and x = −1.
- x + 1 = ±2 gives 1 and −3, not 3 and −1.
- D. u has a maximum value of −2.
- −2 is the leading coefficient, not a value of u.
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