The Quadratic Formula - Concept
A square root is an exponent of one-half. A cube root is an exponent of one-third. Square roots of negative numbers do not have real number roots since the product of any real number and itself is positive. Cube roots do exist for negative numbers since the product of three negatives is a negative. Cube roots re-appear often in Geometry and in Algebra II.
There's lots of different ways to solve quadratics. Some of them you might know, some of them you might not know yet. But my guess is you're going to learn it all in your Algebra class.
One method is by graphing and looking at the x intercepts, but that's not very useful if you get a fractional answer. Sometimes on the graph, it's hard to tell exactly where your line crosses the axis. You could try factoring but factoring doesn't always work. You could try square rooting both sides if there's no b term but that's not always the case.
There's two ways that always work. Those ways are completing the square and the quadratic equation. For many of you this is going to be your favorite method because it always works. But be careful because there's lots of ways to make errors in this situation especially when it comes to the negative signs.
So, your math teacher is going to make you memorize this. It's kind of a bummer. All Math students at some point or another have to memorize this. Your parents probably have this memorized. But here's the good thing. There's a couple of different songs. So I'm going to sing for you, are you ready?
La la la la la warm up warm up, okay. So, my personal favorite version of this is pop goes the weasel, ready? Teren teren ta ta x=-b plus or minus square root of b squared minus 4ac all over 2a. That's pretty good, huh? Let's do it again, ready? Here we go. Everyone sing I want to hear you. Ready, set, go. x=-b plus or minus square root of b squared minus 4ac all over 2a. I'm going to do it one more time just so you guys are annoyed and it starts going through your head and here we go. x=-b plus or minus square root of b squared minus 4ac all over 2a. Okay, yeah. So that's pretty good. You'll be singing that in your sleep.
Another way you could do this is jingle bells. So this works better seasonally. If you guys are learning this around the holiday season, you might want to choose the jingle bells option. Ready? I think I know this one. Okay here we go. Teren teren ta huh okay. x=-b plus or minus square root of b squared minus 4ac all divided by 2a hey! x=-b plus or minus square root of b squared minus 4ac all divided by 2a hey!
Okay, so you guys can choose if you want to be pop goes the weasel or jingle bells kinds of people. Start humming this during your test and your teachers will go crazy but they'll know where you're coming from.
So that was kind of dorky of me I know, but it's really important that you guys memorize this. If you don't want to do the song, write it on your hand for a week until it starts getting engraved in your brain or you could put in an index card, put it in a plastic baggie and hang it in your shower, whatever. Whatever you need to do until you get this in your brain. You just got to do it, there's no way around it.