How to estimate ln(1.1) using quadratic approximation? So the general idea for quadratic approximation is assuming there a function $Q(x)$ we want to estimate near $a$: 
$Q_a(a) = f(a)$
$Q_a'(a) = f '(a)$
$Q_a''(a) = f ''(a)$
But then how do you derive the function $Q_a(x) = f(a) + f '(a)(x-a) + f ''(a) (x-a)^2/2$?
Or can you estimate just using the above one?

What you wrote is the formula for quadratic approximation, which is derived from Taylor series. 
In your case, you need to set $f(x)=\ln x$ and $a=1$, then use the formula.
