In calc, we are studying parabolization. It is the linerazation of a parabola. The linerazation of a standard line is L(x) = b0+b1(x-a) when f(x) is at x=a

b0 = f(a)

b1=f'(a)

The parabolization of f(x) at x=a is given by the equation

P(x)=c0+c1(x-a)+c2(x-a)^2.

f(a) = P(a)

F'(a) = P'(a)

f''(a) = P''(a)

I need to find a formula for c0, c1, and c2 in terms of f(a), f'(a) and f"(a)

Im sure that I need to find the first and second derivitive of the equation

L(x)=c0+c1(x-a)+c2(x-a)^2. Im just not sure where to start...

I believe that c0=f(a), c1=f'(a), and c2=f"(a), but Im not sure if that helps.

Thanks!

Matt