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:

Step1: Recall parabola symmetry

Parabolas are symmetric about their axis of symmetry. For parabolas with vertices on the y - axis (in the form \(x = a(y - k)^2+h\) where \(h = 0\) for these cases as vertices are \((0,4)\) and \((0, - 4)\)), the axis of symmetry is the y - axis (\(x = 0\)).

Step2: Analyze intersection points

Since parabolas are symmetric about their axis of symmetry, if two parabolas intersect and their axes of symmetry are the y - axis, the points of intersection are equidistant from the y - axis. Just because one parabola opens downward doesn't mean the second one must open downward. Also, there is no information to suggest the intersection points are on the x - axis or that the second parabola opens upward.

Answer:

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