SOLUTION: Hello, tutors my homework assignment question is for college algebra. Response to the following: Quadratic equations can be solved by graphing, using the quadratic formula, comp

Question 135036: Hello, tutors my homework assignment question is for college algebra.
Response to the following: Quadratic equations can 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? Why?) Thanks inadvance for your great work and assitance.
Roosevelt
Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!
Great question.
Some folks are more 'visual' than others. Folks that need to see things do well with graphical representations. Also, students with a bent toward geometry like graph. Graph are also a great way to link algebra with geometry.

The quadratic equation will 'always get you an answer if there is one'. But it requires more arithmetic and, IMHO, presupposes that the user understands complex numbers -- since the question of 'what happens when the determinant is negative' is almost certain to be raised. On the other hand, the quadratic equation is easily programmed, so it is a great tool for computer solutions (and also more sophisticated calculators).

Completing the square is an 'OK tool'. But fact is, once one uses it to prove the quadratic equation, I have found few places (outside of problems that specifically state one must use completing the square) where I actually used that method.

Factoring is handy when the the equation are 'fairly simple'. Factoring is very important when polynomial division/multiplication is part of the problem. Plus, factoring is fun and helps students connect algebra to the underlying properties that also apply to arithmetic and also, later on, to more sophisticated algebras.
If you get other responses, can you do me the favor of compiling them and sending the merged ideas to me? I am interested in what others might think.

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