Parabola

Plug in the point \((0,0)\) into the equation. 

 

This gives us: \(0a + 0b + c = 0 \), meaning \(c = 0 \). 

 

Now, plug in the point \((1,2)\) into the equation. This gives us: \(1 =4a + 2b\)

 

Lastly, plug in the point \((1,-2)\) into the equation. This gives us \(1 = 4a - 2b\)

 

Solving this system, we find \(b = 0 \) and \(a = {1 \over 4 }\).

 

Thus, \(a + b + c = \color{brown}\boxed{1 \over 4}\)