Find the quadratic polynomial $g(x) = a x^2 + b x+ c$ which best fits the function $f(x)= 2^x$ at $x = 0$, in the sense that $g(0) = f(0)$, and $g'(0) = f'(0)$, and $g''(0) = f''(0)$.

$g(x) =$
(Using a computer or calculator, sketch graphs of $f$ and $g$ on the same axes. What do you notice?)