Zero
One
Two
More than two
Explanation
Correct answer: C.
Choice C is correct. It is given that the constants and are both positive; therefore, the graph of the given quadratic equation is a parabola that opens up with a vertex on the -axis at a point below the -axis. The graph of the second equation provided is a horizontal line that lies above the -axis. A horizontal line above the -axis will intersect a parabola that opens up and has a vertex below the -axis in exactly two points.
Desmos solution:
Note: Use sliders for a and c with positive values to see the parabola and horizontal line always intersect in two points.
Enter in Desmos:
Reviewed and rewritten by CookSAT
Why the other choices are wrong
Choice A
Choice A is incorrect because the two graphs intersect.
Choice B
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 -axis and the line is above the -axis.
Choice D
Choice D is incorrect because a line cannot intersect a parabola in more than two points.