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