Write the Function in the Form $f ( x ) = a ( x - h ) ^ { 2 } + k$

Multiple Choice

Write the function in the form $f ( x ) = a ( x - h ) ^ { 2 } + k$ by completing the square.
$$g ( x ) = - 3 x ^ { 2 } + 15 x + 2$$

A) $g ( x ) = - 3 \left( x - \frac { 5 } { 2 } \right) ^ { 2 } + \frac { 217 } { 12 }$
B) $g ( x ) = - 3 ( x + 15 ) ^ { 2 } + 2$
C) $g ( x ) = - 3 \left( x - \frac { 5 } { 2 } \right) ^ { 2 } + \frac { 83 } { 4 }$
D) $g ( x ) = - 3 ( x + 5 ) ^ { 2 } - \frac { 2 } { 3 }$