Provide an Appropriate Response $y = a x ^ { 2 } + b x + c$

Provide an appropriate response.
-The curve $y = a x ^ { 2 } + b x + c$ passes through the point $( 2,32 )$ and is tangent to the line $y = 4 x$ at the origin. Find $a$ , $b$ , and $c$ .

A) a = 0, b = 6, c = 4
B) a = 4, b = 0, c = 6
C) a = 6, b = 4, c = 0
D) a = 7, b = 0, c = 0