Advanced MathHardMaximum and zeros from vertex form
Advanced Math practice question
The function w is defined by w(x) = −(x − 4)² + 9. Which statement is true?
- A. w has a maximum of 9 at x = 4, and w(x) = 0 at x = 1 and x = 7.Correct
- B. w has a minimum of 9 at x = 4.
- C. w has a maximum of 9 at x = 4, and w(x) = 0 at x = 3 and x = 5.
- D. w has a maximum of 4 at x = 9.
Answer: A. w has a maximum of 9 at x = 4, and w(x) = 0 at x = 1 and x = 7.
The negative coefficient gives a maximum of 9 at x = 4. Zeros: (x − 4)² = 9, x = 1 or 7.
Why the other answers are wrong
- B. w has a minimum of 9 at x = 4.
- A negative leading coefficient gives a maximum.
- C. w has a maximum of 9 at x = 4, and w(x) = 0 at x = 3 and x = 5.
- x − 4 = ±3 gives 1 and 7, not 3 and 5.
- D. w has a maximum of 4 at x = 9.
- Swaps the vertex's coordinates.
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