solve this quadratic inequality, and we're going to solve it, actually, by graphic. And when we saw quadratic inequalities by graphic, we use like, a hunt of a whole mess of everything we've used. And one of the things we're gonna use is we're going to actually factor as though this were in equation. So pretend instead of the inequalities on this right now says zero, so we can go ahead and we can factor because that's going to go ahead and give us our two points on the X axis. So the factor we need to find two factors of to that add up and give me negative three. Well, the two factors we're gonna be negative two and negative one negative. Two times negative One is positive to Adam. Together I get negative three. So I have X minus two and X minus one equals zero, and I wanna go ahead and solve those. So X minus two equals zero we're gonna add to and X minus one equals zero. We're gonna add one, so X can be to an X can be one. So that's really important to know both of these. So I'm gonna go ahead and I'm gonna put both of those points on my graph on the X axis because on both of those, if I were to plug those values in my wild would actually be zero. Those were the two that make that equation inequality actually true. Okay. Or equation. However it ISS. So now that we've got that, we can also go ahead and we can find a couple of different points so that we can graph our line. Now, I do know that this is a positive. So this is going to be an upward parabolas, so at least I can kind of go ahead and do that. I can also go ahead and find my Y intercept. My y intercept is based on my constant so that my y intercept is going to be positive, too. So right there is my y intercept. I can also find my axes of symmetry, which is, Remember, it's negative. Be over to a. So for this one that's going to be negative. Three over A is once or two, so that's going to be negative. It's a negative negative. So that's actually gonna be positive. So it's positive. Three half, which is really between the one in the to. So it's between those two points so I could go ahead and even draw out my other line to kind of see how this is going to be Now this does say equal to So when I draw my line, I'm gonna draw a solid line throwing out So there would be my parable. Now, when you're writing your solutions, you have to think about compound inequalities. So we're looking at where this is now. Our equation says that this is greater than or equal to zero. That means that our vertex, if it's greater than zero because that's your eggs, that means you would be above the X axis. But this case is actually not. It's below the X axis. So that means that my solutions are gonna be one or the other, but they're not going to be. But because my vertex falls below the X axis, so that means my solution is going to be X is less than or equal toe one or X is greater than or equal to two. If my vertex had been above the X axis, which we're gonna see some in the examples we do, Then we would create a compound where they would be connected by the word and because both statements can be sure.

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## Video Transcript

solve this quadratic inequality, and we're going to solve it, actually, by graphic. And when we saw quadratic inequalities by graphic, we use like, a hunt of a whole mess of everything we've used. And one of the things we're gonna use is we're going to actually factor as though this were in equation. So pretend instead of the inequalities on this right now says zero, so we can go ahead and we can factor because that's going to go ahead and give us our two points on the X axis. So the factor we need to find two factors of to that add up and give me negative three. Well, the two factors we're gonna be negative two and negative one negative. Two times negative One is positive to Adam. Together I get negative three. So I have X minus two and X minus one equals zero, and I wanna go ahead and solve those. So X minus two equals zero we're gonna add to and X minus one equals zero. We're gonna add one, so X can be to an X can be one. So that's really important to know both of these. So I'm gonna go ahead and I'm gonna put both of those points on my graph on the X axis because on both of those, if I were to plug those values in my wild would actually be zero. Those were the two that make that equation inequality actually true. Okay. Or equation. However it ISS. So now that we've got that, we can also go ahead and we can find a couple of different points so that we can graph our line. Now, I do know that this is a positive. So this is going to be an upward parabolas, so at least I can kind of go ahead and do that. I can also go ahead and find my Y intercept. My y intercept is based on my constant so that my y intercept is going to be positive, too. So right there is my y intercept. I can also find my axes of symmetry, which is, Remember, it's negative. Be over to a. So for this one that's going to be negative. Three over A is once or two, so that's going to be negative. It's a negative negative. So that's actually gonna be positive. So it's positive. Three half, which is really between the one in the to. So it's between those two points so I could go ahead and even draw out my other line to kind of see how this is going to be Now this does say equal to So when I draw my line, I'm gonna draw a solid line throwing out So there would be my parable. Now, when you're writing your solutions, you have to think about compound inequalities. So we're looking at where this is now. Our equation says that this is greater than or equal to zero. That means that our vertex, if it's greater than zero because that's your eggs, that means you would be above the X axis. But this case is actually not. It's below the X axis. So that means that my solutions are gonna be one or the other, but they're not going to be. But because my vertex falls below the X axis, so that means my solution is going to be X is less than or equal toe one or X is greater than or equal to two. If my vertex had been above the X axis, which we're gonna see some in the examples we do, Then we would create a compound where they would be connected by the word and because both statements can be sure.

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