and alphabet X equals X square plus eight X plus nine. Now we're gonna graph these, But we're gonna look for a few things, and this way we don't have to do is big of a table. We weren't trying to find points. The first thing we're gonna look for is our Y intercept. This is the point that crosses the line. Well, I can look at my find my c coordinate for that, and that's actually going to be at nine. So when I create my table, I can tell that my ex coordinates gonna be zero and my y coordinate or my f of x coordinate. It's actually gonna be nine, because that is my y intercept. So there's my first point on here. The second thing I confined is I can go ahead and find where my vertex is by finding my axis of symmetry. Remember, you're gonna find the X coordinates for your axis of symmetry, and that's you're gonna find that by saying at X equals my B over negative, too. Tom's a My baby is eight over negative, too. Times my a is one. So I have eight over negative to, which means that X equals four negative four. So I'm gonna go ahead and make sure that that is another point on my graph. And when I plug in negative four, I'm going to get negative seven, and that is going to be my Vertex. From there, I can pick a few other points Thio use for my parabola. So let's pick. Um, looks like as I went negative, I went further away. So let's pick. Let's see, let's do the number. Let's do negative one. So that would be negative. One squared plus eight times negative one plus nine, which would be one minus eight plus nine. And that's going to be negative. Seven plus nine, which is going to be, too, so we can use those points right there. We could do some more if we want Thio, but let's use those. So we have 09 which we already know. It's gonna be my y intercept. Negative four negative seven and negative one. Mhm. Positive, too. So let's graph these points. Well, we have 09 we have negative four negative seven and then we have negative one positive to. Now, if you'll notice. I don't really have ah full parabolas just going up. But I also know that this is my vertex, which means that at this point, this is the point that my line changes. So that tells me that from here I can draw it going up the opposite way. And so there's my parable.

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## Video Transcript

and alphabet X equals X square plus eight X plus nine. Now we're gonna graph these, But we're gonna look for a few things, and this way we don't have to do is big of a table. We weren't trying to find points. The first thing we're gonna look for is our Y intercept. This is the point that crosses the line. Well, I can look at my find my c coordinate for that, and that's actually going to be at nine. So when I create my table, I can tell that my ex coordinates gonna be zero and my y coordinate or my f of x coordinate. It's actually gonna be nine, because that is my y intercept. So there's my first point on here. The second thing I confined is I can go ahead and find where my vertex is by finding my axis of symmetry. Remember, you're gonna find the X coordinates for your axis of symmetry, and that's you're gonna find that by saying at X equals my B over negative, too. Tom's a My baby is eight over negative, too. Times my a is one. So I have eight over negative to, which means that X equals four negative four. So I'm gonna go ahead and make sure that that is another point on my graph. And when I plug in negative four, I'm going to get negative seven, and that is going to be my Vertex. From there, I can pick a few other points Thio use for my parabola. So let's pick. Um, looks like as I went negative, I went further away. So let's pick. Let's see, let's do the number. Let's do negative one. So that would be negative. One squared plus eight times negative one plus nine, which would be one minus eight plus nine. And that's going to be negative. Seven plus nine, which is going to be, too, so we can use those points right there. We could do some more if we want Thio, but let's use those. So we have 09 which we already know. It's gonna be my y intercept. Negative four negative seven and negative one. Mhm. Positive, too. So let's graph these points. Well, we have 09 we have negative four negative seven and then we have negative one positive to. Now, if you'll notice. I don't really have ah full parabolas just going up. But I also know that this is my vertex, which means that at this point, this is the point that my line changes. So that tells me that from here I can draw it going up the opposite way. And so there's my parable.

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