Towards Simpson's Rule
The filled red point can be moved to positive integer values of and integer values of .
The unfilled point is restricted to the -axis but can be moved up and down.
The unfilled point is dependent on but can be moved up and down.
Task 1: Show that the equation of the parabola is .
Task 2: Show that .
Task 3: If all three points are translated so that , and , what happens to the area under the curve?