Find the Equation of the Parabola $y = a x ^ { 2 } + b x + c$

Multiple Choice

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

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