Find a second degree polynomial f(x) (of the form ax2+bx+c) such that f(0)=−1, f′(0)=4, and f′′(0)=1

Answer 1

The polynomial p(x)=(1/2)x^{2}+4x-1 satisfies, p'(x)=x+4 and p''(x)=1 and so p(0)=-1, p'(0)=4 and p''(0)=1.