Chapter 6.1, Problem 76PE

(a)

To determine

The linear system of equation to solve for a, b, and c, which satisfies the function $f\left(x\right)=a{x}^2+bx+c$, the provided values of the function at perticular values are $f\left(3\right)=6.95,f\left(-2\right)=20.2$, and $f\left(12\right)=39.8$.

(b)

To determine

To calculate: The reduced row-echelon form of augmented matrix using graphing utility, which satisfies the function $f\left(x\right)=a{x}^2+bx+c$, the provided values of the function at perticular values are $f\left(3\right)=6.95,f\left(-2\right)=20.2$ and $f\left(12\right)=39.8$.

(c)

To determine

The function of the form $f\left(x\right)=a{x}^2+bx+c$ that fits the data $f\left(3\right)=6.95,f\left(-2\right)=20.2$ and $f\left(12\right)=39.8$.