Use a System of Equations to Find the Specified Equation $y = a x ^ { 2 } + b x + c$

Use a system of equations to find the specified equation that passes through the points. Solve the system using matrices.
Parabola: $y = a x ^ { 2 } + b x + c$

A)
$$y = x ^ { 2 } - 3 x + 4$$
B)
$$y = - x ^ { 2 } - 3 x + 1$$
C)
$$y = - x ^ { 2 } + 3 x + 4$$
D)
$$y = - x ^ { 2 } + 3 x + 1$$
E)
$$y = - x ^ { 2 } - 2 x + 1$$