How do you solve x^2-1=0 by graphing

If you're able to plug it into your graphing calculator and graph it that way, do that and then find where x=0 (or where it intersects the x axis).

If you can't use your graphing calculator, first recognize it is only a transition from the graph of x^2, which is a parabola having a minimum at (0,0). The "-1" would move the entire graph down one point, therefor the new minimum being at (0,-1). Then find where x=0.