What is the quadratic equation and what does it do?
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So I want to preface this that you’re asking about a specific math thing when you don’t have a good grasp on math so this is gonna be a bit tricky for you to get. It’s like you’re asking about what makes a specific guitar solo good when you don’t know what notes are. It’s gonna be a bit hard to get.
But I’ll try anyway (and there’s no shame in not knowing something!)
We can use an equation to represent the world around us. For example, say that I have three apples. Then I get two more apples. I now have five apples. I can represent that like this:
3+2=5
That’s a basic equation and is what most people think of when it comes to math. But that’s not all we can do. Sometimes there is an unknown, and we need to solve for it.
3+2=?
Now there’s an unknown in our equation. We don’t know what that question mark is until we solve for it. But the question mark doesn’t have to be at the end!
3+?=5
Now we have a slightly more complicated situation, we can’t just add the numbers together. We need to figure out how to set up the numbers and move them around so we can get the unknown. But sometimes things are a bit more complicated.
Imagine that you wanted to see not just how many apples you have, when you get two apples, but how many apples you have if someone keeps giving you apples, 2 every second. You can’t just do that like you did the previous time, because how many apples you have depends on how many you had when the previous guy gave you apples. So you need to set it up like this:
3 +2(the number of times given apples)=?
This is three (how many apples we start with) plus 2 apples, times the number of times someone gave us apples. But this is kind of long to write. Let’s simplify this by using place holders. Let’s use “x” instead of that long bit in the prentheses, and y instead of a question mark.
3+2x=y
Swapping it around, y=2x+3
This is a basic algebraic equation this is a linear equation. It describes something that has ONE thing that changes. In this case, it’s apples over time. Anything you could describe as something per something else is this kind of equation. Miles per hour for example.
Now it gets more complicated if you want to measure something that changes how fast it’s changing. For example, if you’re looking at how far you’ve gone in a car. You don’t drive at the same speed the whole time, so you can’t use the same kind of formatting. I’m not going to get into the specifics, but an example of how this equation would work is:
y=6(x^2)+5x-2
Now those numbers are fine for this case, but what if the numbers are different? If we want to talk about this kind of format more generically, we need placeholders. We could just use # instead of the number, but what if we want to talk about the first number specifically? Let’s give each one a letter.
y=a(x^2)+bx+c
Now if we want to know what that unknown “x” is, we need to rearrange it into the quadratic equation. This lets us figure out what that number is if it would be really hard otherwise. Hopefully that was helpful!
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