Here en.wikipedia.org/wiki/Taylor_theorem i have found that linear approximation of f at the point a is
$P_1(x)=f(a)+f'(a)(x-a) $
For the quadratic approximation the quadratic polynomial is
$P_2(x)=f(a)+f'(a)(x-a)+\frac{f''(a)}{2}(x-a)^2 $
Please explain me how did we get the 1/2 multiplier near the second derivative.