I am learning about Linear and Quadratic approximation.
Quadratic Approximation Formula:
$Q(x) = f(a)+f'(a)(x-a)+\frac{f"(a)}{2}(x-a)^2$
Linear Approximation Formula:
$f(x) = f(a)+f'(a)(x-a)$
I am being told to sketch the graph of $f(x) = (9+x)^2$, as well as the linear and quadratic approximations of $f(x)$ at x = 0.
I am confused how to find the "a" in the formula. But here is what I do know, with x = 0:
$f(0) = 81$
$f'(x) = 2(9+x)$
$f'(0) = 18$
$f''(x) = 2$
$f''(0) = 2$
But, I can't plug this into the formula, because I didn't find "a", right?