If you know linear approximation, then quadratic approximation has a similar formula so it shouldn't be hard for you. Quadratic approximation is ONLY used when higher accuracy is neccesary. The formula for linear approximation is L(x)=f(a)+f'(a)(x-a), and the quadratic approximation formula is just that formula plus f''(a)((x-a)²)/2.

The full formula is : Q(x)=f(a)+f'(a)(x-a)+f''(a)((x-a)²)/2.

Be advised, since this is quadratic approximation, we don't care about terms that is higher than 2nd degree. For example we throw away terms like x³.