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[-/1.87 Points]DETAILSHARMATHAP12 2.2.009.belenlne whether Ine (unction $ vertexmd %mum poL 0ianleum? point:The vettex vcrtctAaymm point,minlmum polnt.Find thie â...

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[-/1.87 Points]DETAILSHARMATHAP12 2.2.009.belenlne whether Ine (unction $ vertexmd %mum poL 0ianleum? point:The vettex vcrtctAaymm point,minlmum polnt.Find thie €oore WalesIu pont,( K)F0(FInd tha Icto", Il Any exlst_ (Entor Yuui Anewieig~Loinmia Scpaialed ItAntn doesexlst, #nle DNI )Find (ne V-Inlercept

[-/1.87 Points] DETAILS HARMATHAP12 2.2.009. belenlne whether Ine (unction $ vertex md %mum poL 0i anleum? point: The vettex vcrtct Aaymm point, minlmum polnt. Find thie €oore Wales Iu pont, ( K) F0( FInd tha Icto", Il Any exlst_ (Entor Yuui Anewieig ~Loinmia Scpaialed It Antn does exlst, #nle DNI ) Find (ne V-Inlercept



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$\triangle A B C$ has vertices $A(0,1), B(3,1),$ and $C(1,3) . \triangle D E F$ has vertices $D(1,-1)$ and $E(7,-1) .$ Find two different locations for vertex $F$ so that $\triangle A B C \sim \triangle D E F .$

All right, so we're looking for the Vertex point of a quadratic equation given in standard general form. So for this, we need to know some important buttons on her calculator. So the 1st 1 is there. Why equal button that allows us to actually enter our equation in there. 2nd 1 is our calculate button that allows us to find values on the graph we've actually graft. And then if you want to graph it at any time, you can just hit the graph button, and it will graph it for you. So my very first step is I'm going to go into why equals and I'm going to type out my equation. I'm gonna go negative X squared plus X less seven. And I can put it right into the X one. No, make sure you're using the negative and not the subtract key for this. It will. Some. It will mess up your graphs later on. If you've got it coming second or other things like you're multiplying. So just make sure you're raising the right negative now, So you get into that habit for later from there, we're gonna get into the calculate menu. So to do that. We use second and then trace, and that gets us into this calculate menu because my graph opens downwards because my day is negative. I'm looking for the highest value of my graph, so I'm gonna use the maximum function, and it's very similar to the minimum function. Just the maximum finds us. The highest point in the minimum finds us the lowest point. So once we hit that, it's going too graphic for us. And we're going to see her graph on the very first question asks us is to list a left bound. So all I'm gonna do is I'm gonna pick an X value on the left, and it could be any X value I want. So, for example, I could pick X equals negative, too. And I'm just gonna You'll see it, you'll tape it right in there, and then you're gonna hit. Enter. What you'll see Show up is you're going to see a little extra up around negative too, and you're gonna see a arrow pointing to the left. Now it's gonna ask you to do the right bound. So we're gonna pick an X value on the right again. It does not matter what you pick, it just has to be on the right of the highest point. So, for example, I'm gonna pick X equals three and then I'm gonna hit Enter. What I'll see then show up is I've got my little Exxon to have got my little X on three I've got my arrow pointing to the left I've got my arrow pointing to the right And now it's gonna ask me to guess You can guess if you want or you can just hit the enter key. So once it does that you're gonna get a blinking, um, little blinky narrow here at the very, very top right there and it's gonna give you some values here. So what mine says for me is 0.4999 and 7.25 for my wife. If I notice it's a bunch of nines repeated nines like that, then I could say my Vertex is actually at 0.5 and then my y value of my vertex says it's 7.25 If I wanted to, I could write that infractions. So that would be 1/2. And that would be 29/4, but that's how we can use it. It's the exact same as the minimum button. Just we're using a maximum button because we're looking for the highest value instead of the lowest value this time.

All right, so we're looking at using a graphing calculator to be able to find a vertex point. So there's a couple menus and buttons you're going to need to be familiar with on your calculator on. I'll walk you through the process of what it would look like. Whether you have the 84 the 83 uh, so different color. They all kind of run the same way it's. The very first thing you need to do is you need to find certain buttons on your calculator and they're on the top line. So one of the important ones right here is the Y equals button. That's what we're gonna use in order to intern equation. The other one you're gonna want to use and be familiar with is the calculate button that's gonna find us information about the graft that we might find useful. And then the graft button is also important. If you want to see what your graph looks like, if you hit graph, it will graft your equation. It's the very first step is you're gonna go to why equals. So that's your first step go. Why equals and enter your equation so right under. Why one? We're just gonna write the equation two X squared minus X. Pull us one from there because we want to find the Vertex point. We do need to know what the graph looks like. This graph opens upwards because you're a is positive, which means I'm going to be looking for the lowest point on my graph. So when I go into the trait or calculate menu and to do that, I go the second button and then I hit Trace. It's going to get me to a menu that looks a little bit like this. Calculate value, zeros, minimums, maximums, intersex and so on. Because I'm looking for the lowest point, I'm gonna look for the minimum value of the grass so you can either hit number three to get to that. Or you can scroll down and highlighted and hit Enter. That's your choice once you do that. And even if you didn't hit graft, first do your very first screen, then is going to come up here and it's going to Graff your function and you'll see in the top left corner. It writes out your function that it's graphing and then on the bottom, It says, Left bound and it's got X and Y possible values. And then that's we see the graph on the screen as well. So for left bound, we just need to put any number that is, to the left of the lowest point. So I can see any of my negatives or to the left. So I'm just gonna write a negative one there and hit. Enter. So you're just gonna go X equals negative one and hit. Enter. What you'll see now is it's going to give you a little black triangle that is pointing to the left, and it's also going to give you and X on that spot where you had your value for X equals negative one. We're going to do the same thing for the right bounce. We just have to pick any value that's on the right hand side. I'm gonna pick four, and then I'm just gonna hit enter again. What we'll see now is we've got the little arrow on the left and we'll see a little arrow on the right, which means that our answer is between that, we'll see one X there and we'll see an X at the four value and then you're last up is to guess. You can guess whatever you want, you can just hit. Enter. That's your choice. So really, we're just gonna hit enter, And then what it will do is it will give you a little blinking cursor here, right at your Vertex, and it will tell you your value. So in this case, my value, it says, is 0.24999 You're a 0.24 999 eight and my wife value is zero 0.875 So what we would say then is we would round that and we would say our Vertex is at 0.25 and 0.875 if you want. You can also switch that into fractions so you can just use your math Frackman you to do that. And you'd get 1/4 for the X, and you would get 7/8 for the why. That's how we can use our graphing calculator to find the minimum value. And the minimum value in this case is my Vertex point.

We have 30 number problem. The focus is given as zero comma minus one by two and vortexes off course given they're starting zero comma zero. So let s just This is X. This is where zero comma minus one by two. So focus is this parable. I will be like this. So a standard question must be excess squared equal to minus four B y. Now this is zero comma. Be so we have. Is there going minus B? So we have be equal to one by $2. Plugging people one by two. Well, Helling, except squared equal to minus four into one by two and two p not B y. So excess square equal to minus two times minus two. By this is very question. Thank you so much.

So if we're ever given a quadratic in this form we have a constant A. Where should actually say A is not equal to zero, multiplied by x minus H squared where each is another constant and then plus K. Um whenever we have a function this form, this is a quadratic function in the form that this is in is called vertex form. And so the reason that it's called vertex form is because we're able to just look at this function and figure out the vertex or it gives us the vertex as part of the function and the vertex is going to be a church comma K. So it's H comic K is our vertex. So we have x minus H. Um That means that we have each comic A. If it's X plus H then we have negative H comma K. And so on. If it's minus K then we have um negative K and if it's plus that it's positive. So here are vertex is each comic.


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