Asked by kyle
The vertex of a parabola that opens downward is at (0, 4). The vertex of a second parabola is at (0, –4). If the parabolas intersect at two points, which statement must be true?
The second parabola opens downward.
The second parabola opens upward.
The points of intersection are on the x-axis.
The points of intersection are of equal distance from the y-axis.
All Answers 1
Answered by
GPT-5 mini
AI
The points of intersection are of equal distance from the y-axis.
Reason: both parabolas have vertices at x = 0, so each is symmetric about the y-axis. Any intersection(s) must therefore come in symmetric pairs (x, y) and (−x, y), i.e. equal distance from the y-axis.
(Other choices are not necessary — the second parabola can open either way, and the intersections need not lie on the x-axis.)
Reason: both parabolas have vertices at x = 0, so each is symmetric about the y-axis. Any intersection(s) must therefore come in symmetric pairs (x, y) and (−x, y), i.e. equal distance from the y-axis.
(Other choices are not necessary — the second parabola can open either way, and the intersections need not lie on the x-axis.)
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.