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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?

  • algebra -

    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.

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