Drag the blue and green dots to form two non-intersecting parabolas - a blue f(x) and a green g(x).[br][br]What are possible expressions for f(x) and g(x)?[br]How can you tell from the expressions that f(x) and g(x) do not intersect?[br][br]Now check the 'build a "between" parabola' check box.[br]Drag the yellow dots to make a parabola p(x) such that f(x) < p(x) < g(x) for all x.[br][br]What is a possible expression for p(x)?[br]How can you tell from the expressions that p(x) is between f(x) and g(x) for all x?[br][br]How many possible functions, p(x), are there? How do you know?[br][br][color=#ff0000]What other questions [could,would] you ask?[/color]