Writing in mathematics

Question

When given a quadratic equation, there are many method used for solving. One can use graphing, factoring, completing the square, and the quadratic formula to name a few. Write a brief essay describing when it is best to use each of the 4 method when solving quadratics be used for in the real world? Provide examples to explain.

Answer 1

Hi Joanna,

I can provide a brief overview of how I think these methods are best applied.

GRAPHING: this I would only use if I needed an approximate answer. Unless the intercepts are integers it is difficult to get an accurate answer. It can be helpful though when factoring if you are stumped on which factor pair to try.

FACTORING: This is the first thing that I try with any quadratic. If the leading coefficient of the x² is not equal to 1, I divide everything by the a term to make my life easier. I like an ax²+bx+c=0 where a=1

If there are two nice integer solutions this method works great. That is not true if you are factoring by grouping, that is a little more complicated and in those cases I generally default to the quadratic equation.

COMPLETING THE SQUARE: I have never met anyone who likes this method haha, it is not the fastest or easiest way to get an answer but is important when you want to describe a quadratic in vertex form. This is useful when asked to describe how a quadratic is shifted in a direction or how wide it is.

QUADRATIC FORMULA: This is the most applicable method. It works even when the solutions of x are not nice integers. I would always try to factor before but if that isn't easily done we can always use this method to yield a result.