Advanced MathEasy–MediumFunction from its x-intercepts
Advanced Math practice question
Which of the following functions has a graph in the xy-plane with x-intercepts at x = −1 and x = 4?
- A. y = (x + 1)(x − 4)Correct
- B. y = (x − 1)(x + 4)
- C. y = (x + 1)(x + 4)
- D. y = x² − 4
Answer: A. y = (x + 1)(x − 4)
A factor of (x + 1) gives a zero at x = −1, and (x − 4) gives a zero at x = 4. Check: (−1 + 1)(−1 − 4) = 0 and (4 + 1)(4 − 4) = 0.
Why the other answers are wrong
- B. y = (x − 1)(x + 4)
- (x − 1)(x + 4) has zeros at x = 1 and x = −4 — the signs are reversed.
- C. y = (x + 1)(x + 4)
- (x + 1)(x + 4) has zeros at x = −1 and x = −4.
- D. y = x² − 4
- x² − 4 has zeros at x = 2 and x = −2.
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