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

Multiple Choice

Provide an appropriate response.
-The curves $y = a x ^ { 2 } + b$ and $y = 2 x ^ { 2 } + c x$ have $a$ common tangent line at the point $( - 1,0 )$ . Find $a , b$ , and $c$ .

A) $\mathrm { a } = - 1 , \mathrm {~b} = 1 , \mathrm { c } = - 2$
B) $a = 1 , b = - 1 , c = 2$
C) $\mathrm { a } - 2 , \mathrm {~b} = 1 , \mathrm { c } = - 1$
D) $a = 1 , b = 0 , c = 2$