Quadratic equations can be solved by graphing,using the quadratic formula, completing the square, and factoring. What are the pros and cons of the methods. when would each be appropriate?

Answer 1

graphing gives you a ball-park answer, even showing if there are any real solutions

If the equation starts with x^2 and the middle term is even, I ALWAYS use completing the square, it is faster than using the formula and gives you the reduced answer if it is irrational

I often do a quick calculation of the discriminant
b^2 - 4ac on my calculator.
If that answer is a perfect square, then my quadratic will factor,
If the coefficients are single digits I usually look for factors, takes just a few seconds
If the numbers are two digits or "unruly" I just go for the formula way.
This used to be a problem in the past but with today's calculators the difficulty becomes a mute point.