Question

Dear Mitch,

I'm in seventh grade and I have to memorize the quadratic formula. Usually I'm pretty god at memorizing st5uff, but when I remember this one I usually remember it wrong. Can you give me some hints on how to get it right?

Sincerely,

Ted B.

Dublin

Answer

Dear Ted,

I believe I can!

First, just in case someone who is reading this hasn't learned about the quadratic formula yet, it's a very famous and useful tool that helps people find solutions to a certain type of problem and it helps you construct a graph ("plot points") of the solutions to the equation. The specific type of equation we're talking about is called a "quadratic equation" and without going into a full lesson on what that means (as that was not your question) we can just say that it usually can be written in a form arranged like this: ax^2 + bx + c, with the ax^2 being the most important part to make it a quadratic. Why? Because if a is zero, then you don't have the squaring part of it and you won't get the important and well-known "parabola" shaped graph which usually looks either like a bell or an upside down bell. (which just happens to be the shape of the graph that describes almost every 'normal', natural set of data if you use a large enough quantity of data to develop and fill out the picture. So, anyway, back to your question: How to remember the formula for quadratics, which is something that students are often required to do. A good first step is to make sure you have it written down correctly. It should look like this:

         ________
-b +/- ) b^2-4ac

         2a

O.K. At first it can look pretty scary but if we take a closer look and try to remember one part at a time, it can be much easier. How? Using a small collection of mnemonics (which is just a fancy word for memory tricks.) So, if you look at the part that reads "-4ac" you can use a sentence that has words that would rhyme or get you close to the sounds of the numbers: For "- 4ac you should first read it aloud "minus four a c" and think of a boat. Someone asks you what it's used for and you say:

"mine is for a sea"

'minus 4 a c'

It's pointing out the route it's going to take when it escapes the math book in which it is trapped ... that check-like thing attached to the 'root' is the square-root sign.

Why "plus or minus" in front of the square root sign?

Because that's what square roots are. For example, the number 25 has 2 square roots:

5 and – 5.

Finally, the whole thing is "over" 2a.

Which is:

a + a

Why not just one a?

Because 2a = a + a...

And if there were only one a under that whole big fancy fraction like this:

_______________
           a

Then it wouldn't be as reliable; it would definitely be less dependable to stay balanced and not tip over (like a unicycle with one wheel instead of a bicycle with two wheels) but with 2 a's under it, like this:

___________
        a + a

Then it's more likely to be a solid, dependable formula that won't let the boat on top tip over.

Hope that helps,

Mitch

P. S. If not, just learn how to derive the formula from scratch every time you need it. (Which is not much more of a challenge!).

Good luck!