AMC 12 2015a Problem 12

The parabolas $y=ax^2 - 2$ and $y=4 - bx^2$ intersect the coordinate axes in exactly four points, and these four points are the vertices of a kite of area $12$. What is $a+b$?

\textbf{(A)}\ 1 \textbf{(B)}\ 1.5 \textbf{(C)}\ 2 \textbf{(D)}\ 2.5 \textbf{(E)}\ 3