Hey, everyone. We've learned to solve a couple of different types of equations, and now we're going to add a new equation to the mix called a quadratic equation. Now a quadratic equation is going to be a bit more complicated than a linear equation, and it might even seem a bit overwhelming at times. But don't worry, I'm going to walk you through everything you need to know about quadratic equations in the next several videos starting with what a quadratic equation even is and then going into how to solve them. So let's go ahead and get started. Now if you take a linear equation, so like 2x-6=0, and you simply add an x squared term, so if I had a 3x2+2x-6=0, this is now a quadratic equation. A quadratic equation is also called a polynomial of degree 2 because the highest degree or power in my equation is this 2 on my x squared term. So whether you hear it called a quadratic equation or a second-degree polynomial, these two mean the same thing. You're often going to have to write quadratic equations in standard form. And the standard form of a quadratic equation is axx2+bx+c=0, where all of my terms are on the same side of my equation and they're all written in descending order of power. So my very first term, ax squared, has a power of 2, where my second term, bx, I can imagine an invisible one right here, so I have a power of 1. And then my last term is just a constant. There is no power. So I go from 2 to 1 to 0, descending order of power. You're not only going to have to write quadratic equations in standard form but you're also going to have to be able to identify each of those coefficients, a, b, and my constant c. Looking at my example up here, this 3x2+2x-6, if I asked you what a in that equation was, I would be able to say that this 3, since it's the coefficient of my x squared term, is a. Then b is the coefficient of my x term, which in this case is this positive 2. This is b. And then lastly, c, my constant term, is just the constant on the end of my equation. So in this case, it is a negative 6. I always want to make sure that I'm looking at that sign so that I can completely identify my constant or any other coefficient correctly. Let's go ahead and take a look at some other quadratic equations. I want to write each of these in a standard form and then identify what a, b, and c are.

Let's take a look at our first example. Here we have 5x2=x-3. Now to get this in standard form, I want all of my terms on the same side. So I'm going to go ahead and move this x over and then my negative 3 over so they're all on that left side. Now to get rid of the x on my right side, I need to go ahead and subtract it. Now remember, whatever you do to one side of the equation, you have to do to the other. That has not changed. And then I need to get rid of my 3 by adding it. So we'll, of course, cancel on that right side, leaving me on the left side with 5x2-x+3=0 because there is nothing left on that right side. Now I, of course, want these to be in descending order of power. So I have 2, and then my have my invisible one here, and then my 3 doesn't have a term, so I'm good. This is my quadratic equation in standard form, 5x2-x+3=0. Let's go ahead and identify a, b, and c in this equation. So a is going to be the coefficient of the first term of my x squared term. This is also called the leading coefficient because it's the very first coefficient in my quadratic equation. So a in this equation is 5. Then b is the coefficient of my x term. Here I have negative x, which I have an invisible one here, multiplying that x. So my b is negative 1. Then lastly, c, my constant term, is this positive 3 on the end here. So c here is 3, and that's all for that first example.

Let's go ahead and look at one more. Over here, I have -2x2+53=0. Now the first thing we want to do is get all of our terms to one side, and they already are here, so we're good. And then we want to check that they're in descending order of power. Well, my first term has a power of 2, and then my second term is just a constant. There is no power. So they actually already are written in descending order of power. And actually, this is already completely in standard form, so this is my quadratic equation in standard form. Let's go ahead and identify a, b, and c. Now a again is the coefficient of my x squared term. So in this case, I have a negative 2 multiplying that x squared, so that is a. B is the coefficient of my x term. But if I take a look at my equation, I actually don't have an x term at all. So b is actually going to be 0 because this would be like having a plus 0x stuck in that equation, which wouldn't do anything, which is why it's not there. And then c is my constant term, which in this case is actually a fraction, and it is 5 thirds. So it's totally fine for any of our a, b, and c to be a fraction or for b and c to even be 0. As long as I have that x squared term, it is still a quadratic equation. That's all for this video, and I'll see you in the next one.