Mark is solving an equation where one side is a quadratic expression and the other side is a linear expression. He sets the expressions equal to y and graphs the equations. What is the greatest possible number of intersections for these graphs?

At an intersection, the quadratic expression and the linear expression have the same y-value, so they are equal. Setting a quadratic equal to a linear expression gives a quadratic equation, which can have at most two solutions. Therefore, the greatest possible number of intersections is two, choice C.

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