Find an equation of a parabola that has curvature 8 at the origin.

Since we know its a parabola and lets just assume it opens upwards and has origin (0,0) then the equation has to be f (x) = a (x^2). Too find value a, we have to use equation 11 in the textbook.

k (x) = | f'' (x) | / [1 + (f' (x)) ^2]^ (3/2)

where | f'' (x) | = 2a and f' (x) = 2ax

U then simplify equation and use k (0) to get the

k (0) = 2a, but in the question k (0) = 8, so 8=2a, and a is equal to 4, so equation is 4x^2