Advanced MathHardReading intercepts from vertex form
Advanced Math practice question
The function n is defined by n(x) = (x − 1)² − 16. Which statement about the graph of y = n(x) is true?
- A. It crosses the x-axis at −3 and 5 and the y-axis at −15.Correct
- B. It crosses the x-axis at 1 and −16.
- C. It crosses the x-axis at −3 and 5 and the y-axis at −16.
- D. It crosses the x-axis at 3 and −5.
Answer: A. It crosses the x-axis at −3 and 5 and the y-axis at −15.
(x − 1)² = 16 gives x = 5 or −3. n(0) = 1 − 16 = −15.
Why the other answers are wrong
- B. It crosses the x-axis at 1 and −16.
- 1 and −16 are the vertex's coordinates, not intercepts.
- C. It crosses the x-axis at −3 and 5 and the y-axis at −16.
- The y-intercept is n(0) = −15, not −16.
- D. It crosses the x-axis at 3 and −5.
- The signs are reversed; x − 1 = ±4 gives 5 and −3.
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