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Question

A coordinate plane's x-axis ranges from negative 5 to 5 and its y-axis ranges from negative 3 to 7, both in 1-unit increments. A parabola and a line are plotted. The line and parabola intersect at two points. 1 point of intersection is in quadrant 1 and the other is in quadrant 2.

Which of the following shows the solution(s) for this system of equations?

(1 point)
Responses

(−3,0)
and (3,0)
left parenthesis negative 3 comma 0 right parenthesis and left parenthesis 3 comma 0 right parenthesis

There are no solutions.
There are no solutions.

(−2,4)
and (2,4)
left parenthesis negative 2 comma 4 right parenthesis and left parenthesis 2 comma 4 right parenthesis

(0,8)
left parenthesis 0 comma 8 right parenthesis
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Answer 1

To determine the solutions for the system of equations where a parabola and a line intersect, we need to consider the information provided:

• There are two points of intersection, one in quadrant 1 (where both x and y are positive) and one in quadrant 2 (where x is negative and y is positive).

Examining the provided response choices:

1. (−3,0) and (3,0): This pair suggests intersection points at the x-axis, which means y=0 for both, thus they do not fall in quadrants 1 or 2. Therefore, this pair is not correct.

2. There are no solutions: This implies that the line and parabola do not intersect. Since it is stated that there are two points of intersection, this choice is also incorrect.

3. (−2,4) and (2,4): Here, (-2, 4) is in quadrant 2, and (2, 4) is in quadrant 1. This matches the conditions given that there is one intersection in quadrant 1 and one in quadrant 2. This pair is a valid choice.

4. (0,8): This point is only in quadrant 2, thus fails to provide a second intersection point in quadrant 1. Hence, this choice is incorrect.

Based on this analysis, the correct answer is:

(−2,4) and (2,4).