## Algebra and Trigonometry 10th Edition

Published by Cengage Learning

# Chapter 10 - 10.1 - Matrices and Systems of Equations - 10.1 Exercises - Page 712: 88

#### Answer

$f(x) = 2x^{2} + x - 1$

#### Work Step by Step

We must first solve for the functions in terms of a, b, and c: f(1) = a + b + c = 2 f(2) = 4a + 2b + c = 9 f(3) = 9a + 3b + c = 20 We can then form the matrix, and use Gaussian elimination and back-substitution to solve the matrix: $\begin{bmatrix} 1 & 1 & 1 & |2\\ 4 & 2 & 1 & |9\\ 9 & 3 & 1 & |20\\ \end{bmatrix}$ ~ $\begin{bmatrix} 1 & 1 & 1 & |2\\ 0 & -2 & -3 & |1\\ 0 & -6 & -8 & |2\\ \end{bmatrix}$ ~ $\begin{bmatrix} 1 & 1 & 1 & |2\\ 0 & 2 & 3 & |-1\\ 0 & 0 & 1 & |-1\\ \end{bmatrix}$ C: c = -1 B: 2b + 3(-1) = -1 2b - 3 = -1 2b = 2 b = 1 A: a + 1 - 1 = 2 a = 2 Using the solution above, the quadratic function is: $f(x) = 2x^{2} + x - 1$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.