Answer to Question #19255 in Calculus for hsd

Question

Find the second-degree Taylor polynomial for f(x)=2x2−8x+6 about x=0.

P2(x)=

Answer 1

P2(x)=f(0)+f'(0)x+f''(0)x^2/2
f(0)=6
f'(x)=4x-8, f''(x)=4
f'(0)=-8, f''(0)=4
Hence
P2(x)=6-8x+4x^2/2=2x^2-8x+6
As you can see Taylor polynomial coincides with function f(x) because function f(x) is a second degree polynomial itself