Question

Use the image to answer the 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

Answer 1

To determine the correct response regarding the solution(s) for the system of equations represented by the line and the parabola intersecting in quadrants 1 and 2, we need to find ordered pairs that reflect these intersection points.

The information states that one intersection point is in quadrant 1 (where both x and y are positive), and the other is in quadrant 2 (where x is negative and y is positive).

From the given options:

1. **(−3, 0) and (3, 0)** - This is incorrect as both points have a y-value of 0 (neither is in quadrant 2 or 1).

2. **There are no solutions.** - This is incorrect because it contradicts the problem statement that there are two points of intersection.

3. **(−2, 4) and (2, 4)** - This is the correct choice because (−2, 4) is in quadrant 2 and (2, 4) is in quadrant 1.

4. **(0, 8)** - This point is not a solution as it's not where the line and parabola intersect.

Therefore, the correct answer is: **(−2, 4) and (2, 4)**.