Question

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.

Explanation:

1. Parabolas are symmetric about their axes of symmetry. Since both parabolas have vertices on the y - axis (x = 0), their axes of symmetry are the y - axis.
2. When two parabolas intersect, the intersection points are symmetric about the common axis of symmetry (in this case, the y - axis). So, the points of intersection are of equal distance from the y - axis.
3. Just because one parabola opens downward doesn't mean the second one must open downward. For them to intersect at two points, the second parabola could open upward. And we can't be sure the intersection points are on the x - axis.

Answer:

The points of intersection are of equal distance from the y - axis.