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.

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.

Option: A is the correct answer.

A.  The parabola opens downward.

As we know that points with zero are not considered in any quadrant they are considered on axis.

Hence, the upward facing graph can't meet at origin, since the vertex is the minimum point of the upward parabola and hence all the values on the parabola must lie above that.

Also we can't define the slope of a line from this information, the line may have any slope.

Hence, the only possibility is that the parabola opens downward.