The Table Shows the Enrollment Projections (In Millions)for Public Universities $y=a t^{2}+b t+c$

Multiple Choice

The table shows the enrollment projections (in millions) for public universities in the United States for the years 2010 through 2012.
Year
Enrollment projections
2010
13) 83
2011
14) 07
2012
14) 23
The data can be modeled by the quadratic function $y=a t^{2}+b t+c$ .Create a system of linear equations for the data.Let t represent the year,with t = 10 corresponding to 2010.

A) $$\left\{ \begin{array} { l } 100 a + 10 b + c = 13.83 \\121 a - 11 b + c = 14.07 \\144 a + 12 b + c = 14.23\end{array} \right.$$
B) ​ $$\left\{ \begin{array} { l } 100 a - 10 b + c = 13.83 \\121 a + 11 b + c = 14.07 \\144 a + 12 b + c = 14.23\end{array} \right.$$
C) ​ $$\left\{ \begin{array} { l } 100 a + 10 b + c = 13.83 \\121 a + 11 b + c = 14.07 \\144 a + 12 b + c = 14.23\end{array} \right.$$
D) ​ $$\left\{ \begin{array} { l } 100 a + 10 b + c = 13.83 \\121 a + 11 b + c = 14.07 \\144 a + 12 b - c = 14.23\end{array} \right.$$
E) ​ $$\left\{ \begin{array} { l } 100 a - 10 b - c = 13.83 \\121 a - 11 b - c = 14.07 \\144 a - 12 b - c = 14.23\end{array} \right.$$