Chapter 9.1, Problem 76PE

For Exercises 75-76, the given function values satisfy a function defined by $f\left(x\right)=a{x}^2+bx+c$

a. Set up a system of equations to solve for $a$ , $b$ , and $c$ .

b. Use a graphing utility to find the reduced row-echelon form of the augmented matrix.

c. Write a function of the form $f\left(x\right)=a{x}^2+bx+c$ that fits the data.

$\begin{array}{c}f\left(3\right)=6.95\\ f\left(-2\right)=20.2\\ f\left(12\right)=39.8\end{array}$