Question 416744
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?

..

Factoring is the best way to solve quadratic equations if the expression is factorable. For small single-digit coefficients, one can usually determine quickly whether the expression is factorable. If not, completing the square or quadratic formula are appropiate. Again, for single-digit coefficients completing the square might be a quick way to solve. For large, decimal, and fractional coefficients, I would use the quadratic formula. Sometimes it is a good idea to check the discriminant,(b^2-4*a*c)of the quadratic formula. It could reveal the following:
..
If (b^2-4*a*c)>0,the equation will have two distinct real roots. If it turns out to be a perfect square, the equation is probably factorable.
If (b^2-4*a*c)=0, the equation will have one real root, called a double root.
If (b^2-4*a*c)<0,the equation will have no real roots. There would two complex number roots.
..
As for graphing, I think this is one of the best ways to understand and help you retain what you have learned by relating the algebra to a visual representation of what you did. No longer will math be just a bunch of abstract numbers, but  that those numbers represent a special curve or figure you can see on a screen. However,it should not be used it solve equations, but rather to check the algebriac solutions you came up with. I would highly recommend anyone serious about understanding algebra and higher math like calculus learn how to use a graphing calculator.