12. Parabolas $y=a x^{2}-2$, $y=4-b x^{2}$ intersect the coordinate axes at exactly four points, forming a kite with an area of 12. Then the value of $a+b$ is ().
(A) 1
(B) 1.5
(C) 2
(D) 2.5
(E) 3
12. B.

Let the parabola $y=a x^{2}-2$ intersect the $x$-axis at points $A\left(x_{1}, 0\right)$ and $C\left(x_{2}, 0\right)$, and intersect the $y$-axis at point $B(0,-2)$; the parabola $y=4-b x^{2}$ intersects the $x$-axis at points $A\left(x_{1}, 0\right)$ and $C\left(x_{2}, 0\right)$, and intersects the $y$-axis at point $D(0,4)$.
Then $|B D|=6$,
$S_{\text {trapezoid } A B C D}=\frac{1}{2}|A C||B D|=12$.
Thus, $|A C|=4$.
Therefore, $A(-2,0), C(2,0)$.
Hence, $a=\frac{1}{2}, b=1$, so $a+b=1.5$.