In Exercise 8.2.4.5,we found that the degree 2 Taylor polynomial centered ata=0of a quadratic function is the quadratic function itself. In this exercise, weexplore how changing the center of the approximation offers additional insightinto the function.Let f(x)=12x2-2x+5, and let a=2be the center at which we will find adegree 2 Taylor polynomial approximation off.a.By finding f'(x),f''(x),f(2),f'(2), and f''(2), determine T2(x), thedegree 2 Taylor polynomial approximation off that is centered ata=2.b. Plot both f(x) and T2(x)on the same axes. What do you observe?c. What does the algebraic form ofT2(x) tell you about the original functionf(x)?d. What is the tangent line approximation tof(x)ata=2? What is specialabout the function's behavior at this input value?