smc

Clearly, the parabolas must intersect the x-axis at the same two points. Their distance multiplied by $4-(-2)$ (the distance between the y-intercepts), all divided by 2 is equal to 12, the area of the kite (half the product of the diagonals). That distance is thus 4, and so the x-intercepts are $(2,0),(-2,0).$ Then $0=4a-2\to a=0.5$, and $0=4-4b\to b=1.$ Then $a+b=\boxed{1.5}$.