Find the Quadratic Polynomial $y = a x ^ { 2 } + b x + c$

Multiple Choice

Find the quadratic polynomial $y = a x ^ { 2 } + b x + c$ whose graph passes through the points $( - 3,7 )$ , $( - 2,1 )$ , and $( 1,7 )$

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