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What is the intuition behind using this basis? In particular, how does the binomial theorem relate to it?


Are these curves essentially identical to how a line would look if we applied the definition of Bezier curves?


Do these curves all sum to 1 for any given x? I can't recall if you explicitly stated this anywhere in the lecture, but it seems like they should. (Also, if this is true, is this why the Bezier curve is contained in the convex hull, as is mentioned a few slides later? Do we also need the fact that the curves are nonnegative?)


Is it possible to interpolate functions of varying orders, and if so, would there be a scenario in which this would be applicable?


Is there a visual intuition for using these basis functions?


This seems too abstract for me to understand. Can there be a more concrete example (visuals or values) to help understanding this?