Find the second-degree Taylor polynomial for f(x)=2x2−8x+4 about x=0. P2(x)= ___

Answer 1

f(x) = 2x² - 8x + 4

f'(x) = 4x-8

f"(x) = 4

P₂(x) = f(0) + f'(0)(x-0) + [f"(0) / 2!](x-0)² = 4 - 8x + 2x² = f(x)

Note: For a polynomial function f(x) of degree n, P_n(x) (centered at x = 0) is the same as f(x).