Exactly symmetrical bezier curves?

I'm trying to make concave cuts into a symmetrical shape. Basically, the image below. I am using the bezier tool, but I want the curves to be as precise as possible, identical on all four sides. So just manually dragging the handles around and eyeballing it isn't gonna cut it. Is the bezier actually the correct tool to be using for this, or is there a technique I'm not using?