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?

Set the quadratic expression equal to the linear expression. Moving everything to one side produces a quadratic equation, which can have at most two real solutions. Each real solution corresponds to an intersection of the graphs, so the greatest possible number is two.

AI-written and checked against the verified answer.