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

(−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

There are no solutions.
There are no solutions.

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

Answer 1

Given the information that the parabola and the line intersect at two points, one in quadrant 1 and the other in quadrant 2, we can deduce the following from the options provided:

1. The solution (−2, 4) and (2, 4) indicates that both points share the same y-coordinate (4), meaning they would be horizontally aligned and would not fit the given quadrants' conditions, as one point cannot be in quadrant 1 and the other in quadrant 2 if they share the same y-coordinate.

2. The solution (0, 8) suggests a single point above the y-axis in quadrant 1. This means it does not provide two points of intersection.

3. The statement "There are no solutions" contradicts the information given, as we know there are indeed two points of intersection.

4. The solution (−3, 0) and (3, 0) indicates points on the x-axis. One of these points, (3, 0), is in quadrant 1, but (−3, 0) is in quadrant 2. Hence, this option fulfills the requirement of having one point in quadrant 1 and the other in quadrant 2.

Therefore, the correct answer is:

(−3, 0) and (3, 0)