In the equation above, a and c are positive constants. How many times does the graph of the equation above

Question

In the equation above, a and c are positive constants. How many times does the graph of the equation above intersect the graph of the equation in the xy -plane?

Accepted Answer

Choice C is correct. It is given that the constants a and c are both positive; therefore, the graph of the given quadratic equation is a parabola that opens up with a vertex on the y -axis at a point below the x -axis. The graph of the second equation provided is a horizontal line that lies above the x -axis. A horizontal line above the x -axis will intersect a parabola that opens up and has a vertex below the x -axis in exactly two points. Choices A, B, and D are incorrect and are the result of not understanding the relationships of the graphs of the two equations given. Choice A is incorrect because the two graphs intersect. Choice B is incorrect because in order for there to be only one intersection point, the horizontal line would have to intersect the parabola at the vertex, but the vertex is below the x -axis and the line is above the x -axis. Choice D is incorrect because a line cannot intersect a parabola in more than two points.

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