Linear and Quadratic approximations in Calculus 2

179 Views Asked by At

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?