Use the image to answer the question.

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

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

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

Answer 1

To determine the solution(s) for the system of equations represented by the intersection points of the line and the parabola, we need to analyze the information provided.

The question states that the line and parabola intersect at two points, with one point located in quadrant 1 and the other in quadrant 2.

• Quadrant 1 contains points where both x and y are positive (x > 0, y > 0).
• Quadrant 2 contains points where x is negative and y is positive (x < 0, y > 0).

Given the coordinates provided in the response options:

1. (−2, 4) and (2, 4) – Here, the point (−2, 4) is in quadrant 2, and (2, 4) is in quadrant 1, which aligns with the information about the intersections.

2. (0, 8) – This point is not in either quadrant 1 or quadrant 2, as it lies directly on the y-axis.

3. (−3, 0) and (3, 0) – These points are on the x-axis. The point (−3, 0) is in quadrant 2, while (3, 0) is in quadrant 1, but they do not satisfy the requirement for being the intersection points since they have a y-coordinate of 0.

Given this analysis, the correct option that shows the solutions for the system of equations is:

(−2, 4) and (2, 4).