Quadratic equations may be solved by graphing, using the quadratic formula, completing the square, and factoring. What are the pros and cons of each of these methods? When might each method be most appropriate? Which method do you prefer? Explain why.

The graphing method allows you to visualize quadratic equation solutions, since the solution(s) to the equation occur where the graph intersects the x axis. But if you aren't given a graph, this method is tough, since it's tough to come up with an accurate graph. This method doesn't help if the solutions are imaginary. The quadratic formula is a good way to get the answer regardless of the equation. If you can remember the formula, then you can solve any equation you are given, even if the solutions are imaginary. Completing the square is similar, in that if you remember the process, you can always get the answer. Completing the Square can be used to solve any quadratic equation. It also helps in graphing quadratic equations. Some of the cons for this method also involves more steps and can seem a lot more complicated. It is also slower the using the quadratic formula. When the equation is in the form x^2=d, or (x+c)^2=d, or when creating a binomial square is straightforward, then use this method. I think that factoring is the quickest and easiest method, but it only works for "simple" equations that have "nice" solutions. If you aren't good at seeing the factors, this can be very hard. I would use the graphing method if I am already given a graph of the quadratic. The formula and completing the square are useful for equations with more complex (or imaginary) solutions that aren't integers or simple fractions. Factoring is a good way to solve equations with whole number solutions. I prefer to use the factoring method, if I can, since it allows me to come up with the solutions in one easy step. Each of the other methods take longer.