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.

Answer 1

Sometimes the factors just jump out at you , such as in
x^2 + 7x + 12 = 0
Usually, if the coefficients are single digits, it only takes a few seconds to see if it factors.

If the coefficients are 2 digits or more, I do a quick calculation of the determinant b^2 - 4ac
If that value is a perfect square, then I know the quadratic factors, but having found the discriminant, I am over half way there to get the answers, so I keep going with the formula anyway.

If the coefficient of x^2 is 1 and the middle term is even, I will always use completing the square over the formula.
It gives you the simplified radical solution, whereas the formula answer usually has to be simplified

e.g.
x^2 + 8x - 3 = 0
completing the square:
x^2 + 8x + 16 = 3 + 16
(x+4)^2 = 19
x+4 = ± √19
x = -4 ± √19

formula way:
x = (-8 ± √(64 - 4(1)(-3)) )/2
= (-8 ± √76)/2
= (-8 ± 2√19)/2
= -4 ± √19
Completing the square appears easier in this case.