The vertex of a parabola is in the first quadrant of a coordinate grid. A line with a negative slope passes through the origin. If the parabola and line intersect at the origin, which statement must be true?

Write the parabola as y = a(x − h)² + k, where its vertex is (h, k). Since the vertex is in the first quadrant, h and k are both positive. The parabola passes through the origin, so 0 = ah² + k, which gives a = −k/h² < 0. A negative value of a means the parabola opens downward, so “The parabola opens downward” must be true.

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