The Interpolated Polynomial is that unique polynomial that passes through the given points.[br]By calculating some points on a function and working out the associated Interpolated Polynomial we can approximate the curve.[br][br]By imagining being able to calculate with an unlimited number of points and taking a range for those points which tends to zero we can obtain the Taylor Polynomial.[br][br]Use the interactivity below to explore how the Interpolated Polynomial and the Taylor Polynomial are connected.[br][br]Things to explore:[br][list][*]What can you say when the order of the taylor polynomial is 1?[/*][*]Are you surprised by what happens when you reduce the range of points?[/*][*]Which order of Taylor polynomial is best?[/*][*]What happens when you change the function?[/*][/list]