Chapter 5.FR2, Problem 14E

Reminder Round all answers to two decimal places unless otherwise indicated.

Find the quadratic determined by $\left(-1,1\right)$, $\left(0,0\right)$, and $\left(1,1\right)$. (See the suggestion for Exercise 11.)

11. Find the quadratic determined by $\left(1,5\right)$, $\left(-1,3\right)$, and $\left(2,9\right)$. (Suggestion: We are looking for a quadratic $a{x}^2+bx+c$. We need to find $a$, $b$, and $c$.) The fact that the quadratic passes through the three points yields the following system of equations:

$\begin{array}{l}a+b+c=5\\ a-b+c=3\\ 4a+2b+c=9\end{array}$

Solve this system for $a$, $b$, and $c$.