Solve the Problem $y = a x ^ { 2 } + b x + c$

Multiple Choice

Solve the problem.
-Find the equation of the parabola $y = a x ^ { 2 } + b x + c$ that passes through the points $( - 2,4 ) , ( 0 , - 2 )$ , and $( 3,1 )$

A) $y = \frac { 2 } { 15 } x ^ { 2 } + 1 x - 5$

B) $y = - \frac { 7 } { 5 } x ^ { 2 } + \frac { 4 } { 5 } x - 2$

C) $y = \frac { 4 } { 5 } x ^ { 2 } - \frac { 7 } { 5 } x - 2$

D) $y = \frac { 7 } { 15 } x ^ { 2 } - \frac { 14 } { 5 } x - \frac { 2 } { 3 }$