Chapter 1.1, Problem 2WT

Use the result in Exercise 21 to find values of a, b, and c for which the curve $y=a{x}^2+bx+c$ passes through the points (−1, 1, 4), (0, 0, 8), and (1, 1, 7).

The curve $y=a{x}^2+bx+c$ shown in the accompanying figure passes through the points (x₁, y₁), (x₂, y₂), and (x₃, y₃). Show that the coefficients a, b, and c form a solution of the system of linear equations whose augmented matrix is

$\left[\begin{array}{l}{x}_1^2{x}_{1}1y_1\\ x_2^2{x}_{2}1y_2\\ x_3^2{x}_{3}1y_3\end{array}\right]$

FIGURE Ex-21