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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.

2 Answers by Expert Tutors

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Denise W. | Elementary / Middle / High School Math TutorElementary / Middle / High School Math T...
I agree with Paul H.  Some methods are better in some situations that others.
Factoring is the easiest method if the equation lends itself to it.
If I find that factoring is not going to work, I often turn to the quadratic formula next.
I might use a graphing method to determine if the roots I calculated make sense, I'm not sure I would try and do it that way exclusively unless I had a graphical calculator handy.  On the other hand, it is always useful to try and visualize a problem.
Completing the square is just a variation on using the quadratic formula, it takes a little more effort but can be a good way to get the roots.
Hope this helps!
Paul H. | Math, Excel, InDesign, Photography and Computers in GeneralMath, Excel, InDesign, Photography and C...
Well, i suppose that "prefer" is really a subjective answer, meaning it depends on who you ask.
That being said, i think if the equation is easily solved with factoring it is fairly simple and quick with little chance of errrors.....but it isn't always easy.
Graphing works great if the roots are on nice / whole numbers, but if they are not, then you are "guessing" a in my opinion, not hugely accurate.
Completing the square is more complex, but if it is not an easy factoring problem then i prefer it.
Try some with all three methods and see which you like.....there is no right answer for "like". 
Good luck.