I really, really don't like this question. People have preferences in solving quadratics. I would personally use, and would encourage anyone to use the quadratic equation. That's because completing the square would get excessively fractional, graphically doesn't even work because the solutions are imaginary, and differentiating it wouldn't be necessary, as there are no irrational numbers (except i, which is just imaginary). So, in short, quadratic equation because you can't get anything graphically, the answers are ugly fractions, and you can actually use that method.
