## Algebra and Trigonometry 10th Edition

$f(x) = -9x^{2} - 5x + 11$
We must first solve for the functions in terms of a, b, and c: f(-2) = 4a - 2b + c = -15 f(-1) = a - b + c = 7 f(1) = a + b + c = -3 We can then form the matrix, and use Gaussian elimination and back-substitution to solve the matrix: $\begin{bmatrix} 4 & -2 & 1 & |-15\\ 1 & -1 & 1 & |7\\ 1 & 1 & 1 & |-3\\ \end{bmatrix}$ ~ $\begin{bmatrix} 4 & -2 & 1 & |-15\\ 0 & 2 & -3 & |-43\\ 0 & -6 & -3 & |-3\\ \end{bmatrix}$ ~ $\begin{bmatrix} 4 & -2 & 1 & |-15\\ 0 & 2 & -3 & |-43\\ 0 & 0 & -12 & |-132\\ \end{bmatrix}$ C: -12c = -132 c = 11 B: 2b - 3(11) = -43 2b - 33 = -43 2b = -10 b = -5 A: 4a - 2(-5) + 11 = -15 4a + 10 + 11 = -15 4a + 21 = -15 4a = -36 a = -9 Using the solution above, the quadratic function is: $f(x) = -9x^{2} - 5x + 11$