Archimedes (250BCE) discovers the area of a parabola

Find a . cubic . function . f(x) such that f x 2 = 1 + x + other stuff of degree 4 or higher.Use your answers to #3 above to create a Generalized Binomial Theorem for . n= 1 2 . How should 1 / 2 k . be defined?Use your formula from #4 to find a . quartic. function . f(x) such that f x 2 = 1 + x + other stuff of degree 5 or higher. ................
................