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

Multiple Choice

Find an equation of the form $y = a x ^ { 2 } + b x + c$ whose graph passes through the points $( 1,7 ) ,$ $( - 4 , - 18 ) ,$ and $( - 1,3 ) .$

A) $y = - x ^ { 2 } + 2 x + 6$
B) $y = - x ^ { 2 } + 6 x + 2$
C) $y = 2 x ^ { 2 } - x + 6$
D) $y = 6 x ^ { 2 } - x + 2$
E) $y = 6 x ^ { 2 } + 2 x - 1$