Algebra Question
posted by pj .
Quadratic equations can be solved by graphing, using the quadrat completing the square, and factoring. What are the pros and cons these methods? When might each method be most appropriate?

Factoring is quickest and best if simple integer factors are possible
The quadratic equation and completing the square are the same thing as far as I am concerned. This is the way to go if you have a calculator handy and the numbers are too nasty for factoring.
Use a graph if you want to see how the function is behaving as well as its zeros. 
If the numbers are reasonably small the first thing I try is factoring
If the coefficient of the square term is 1, and the middle term is even, then completing the square works great
For all other cases I simply use the quadratic formula, knowing that it always works.
One of my favourite questions when I was still teaching was to give 3 different quadratic equations, using a different method for each.
(The trick was that there was only one that factored, so it you used the quadratic formula for that one, you were out of options for the factoring type.)
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