Taylor Polynomials: Find a0, a1, a2, a3, and a4

[lmannoia]

Homework Statement

Let f(x)=x² +3x -5, and let the summation (from n=0 to infinity) a_n (x-4)ⁿ be the Taylor series of f about 4. Find the values of a0, a1, a2, a3, and a4.

Homework Equations

The Attempt at a Solution

What am I supposed to do with the summation? And what does it mean to find a Taylor polynomial 'about 4'? I'm confused on how to relate both of those things to the f(x) that they gave me.

 

[Mark44]

Homework Statement

Let f(x)=x² +3x -5, and let the summation (from n=0 to infinity) a_n (x-4)ⁿ be the Taylor series of f about 4. Find the values of a0, a1, a2, a3, and a4.

Homework Equations

The Attempt at a Solution

What am I supposed to do with the summation? And what does it mean to find a Taylor polynomial 'about 4'? I'm confused on how to relate both of those things to the f(x) that they gave me.

You are supposed to write f(x) = x² + 3x - 5 as a power series in powers of (x - 4) instead of in powers of x. Since the function is of degree two, your Taylor's series will also be of degree two. IOW, it will be f(x) = a₀ + a₁(x - 4) + a₂(x - 4)².