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?

A. The parabola opens downward.

B. The parabola opens upward.

C. The slope of the line is equal to - 1.

D. The slope of the line is not equal to - 1.

Question

Pierce Lawrence

Mathematics

26 February, 21:25

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?

A. The parabola opens downward.

B. The parabola opens upward.

C. The slope of the line is equal to - 1.

D. The slope of the line is not equal to - 1.

+2

Answers (1)

Know the Answer?

Aliya Allison · Answer 1

The correct answer is:

A) The parabola opens downward.

Explanation:

Since the vertex of the parabola is in the first quadrant, it must not be at the origin. This means that the line does not intersect the parabola at the vertex.

Since the vertex of the parabola is not at the origin and is in the first quadrant, if it opens upward, it will not intersect the line. Even if the vertex is at (1, 0), the parabola will open above (0, 0). This means in order for it to intersect the line at the origin, it must open downward.