Write a System of Linear Equations in Three Variables, and Then

Multiple Choice

Write a system of linear equations in three variables, and then use matrices to solve the system.
-The table below shows the number of birds for three selected years after an endangered species protection program was started. $$\begin{array} { l | c c c } \mathrm { x } \text { (Number of years after 1980) } & 1 & 5 & 10 \\\hline \mathrm { y } \text { (Number of birds) } & 43 & 139 & 349\end{array}$$ Use the quadratic function $y = a x ^ { 2 } + b x + c$ to model the data. Solve the system of linear equations involving $a , b$ , and $c$ using matrices. Find the equation that models the data.

A) $y = 2 x ^ { 2 } + 12 x + 29$
B) $y = 3 x ^ { 2 } + 24 x + 24$
C) $y = 4 x ^ { 2 } - 12 x + 32$
D) $y = 4 x ^ { 2 } - 36 x + 25$