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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

(−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.
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

Answer 1

Based on the description given, the parabola and line intersect at two distinct points, one in quadrant 1 and the other in quadrant 2. The options provided are:

1. (0,8)
2. (−2,4) and (2,4)
3. There are no solutions.
4. (−3,0) and (3,0)

From the information you provided, the intersection points cannot be (0,8) because that point lies outside the given range of the y-axis (which goes only to 7).

The points (−2,4) and (2,4) are both in quadrant 2 and do not satisfy the quadrant distribution (one point in quadrant 1 and another in quadrant 2).

The option stating "There are no solutions" is not valid since it’s indicated that the line and parabola do intersect.

Lastly, the points (−3,0) and (3,0) both lie on the x-axis and suggest intersections, but they are outside the defined points of intersection of one in quadrant 1 and another in quadrant 2.

Given that neither option completely satisfies the conditions of the intersections provided. However, the best option that indicates two intersection points, even though they might not perfectly match the quadrants described, is: (−2,4) and (2,4), as that indicates two intersections are occurring, albeit without adhering to the defined quadrants.