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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

(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

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

There are no solutions.

Answer 1

Based on the description of the coordinate plane and the information provided about the intersection points being in quadrants 1 and 2, we need to look for coordinates that fit this criterion.

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

Now, let's analyze the given options:

1. (0, 8): This point is in Quadrant 2 because x=0 and y=8. However, it does not represent two points of intersection.

2. (−3, 0) and (3, 0): This pair of points lies on the x-axis (where y=0), which is not in any quadrant. Therefore, this option is incorrect.

3. (−2, 4) and (2, 4): Here, (−2, 4) is in Quadrant 2 (x < 0, y > 0) and (2, 4) is in Quadrant 1 (x > 0, y > 0). This set of points meets the requirement of having one intersection in Quadrant 1 and one in Quadrant 2.

4. There are no solutions: This is not true because we have identified at least one pair of intersection points.

Given this analysis, the correct response that shows the solution(s) for the system of equations is:

(−2, 4) and (2, 4).