Advanced MathMediumParabola from its direction and x-intercepts
Advanced Math practice question
Which of the following could be the equation of a parabola in the xy-plane that opens downward and has x-intercepts at x = −1 and x = 3?
- A. y = −(x + 1)(x − 3)Correct
- B. y = (x + 1)(x − 3)
- C. y = −(x − 1)(x + 3)
- D. y = (x − 1)(x + 3)
Answer: A. y = −(x + 1)(x − 3)
x-intercepts −1 and 3 need factors (x + 1) and (x − 3); opening downward needs a negative leading coefficient.
Why the other answers are wrong
- B. y = (x + 1)(x − 3)
- Right intercepts, but it opens upward.
- C. y = −(x − 1)(x + 3)
- Opens downward, but its intercepts are 1 and −3.
- D. y = (x − 1)(x + 3)
- Wrong intercepts and opens upward.
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