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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

Based on the information provided, there are two points of intersection between a line and a parabola, with one point located in quadrant 1 and the other in quadrant 2.

Quadrant 1 has coordinates where both x and y are positive (x > 0, y > 0), while quadrant 2 has coordinates where x is negative and y is positive (x < 0, y > 0).

Given the responses available:

• (−3,0) and (3,0): These points are on the x-axis, and both y-values are 0, which does not fit the description of the intersection points.
• There are no solutions: This contradicts the information provided, as the problem states there are intersections.
• (−2,4) and (2,4): This choice has one point in quadrant 2 (−2, 4) and one in quadrant 1 (2, 4), which fits the description perfectly.
• (0,8): This point is only in quadrant 1 and does not provide two points of intersection.

The correct answer showing the solutions for the system of equations is:

(−2,4) and (2,4).