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QUESTION }[email protected] peld Determine the zeros; vertical asymplotes and end behawor ol each of the following functions Justify your Anuwum 2* + 9 X-9 X -9 2* + 9...

Question

QUESTION }[email protected] peld Determine the zeros; vertical asymplotes and end behawor ol each of the following functions Justify your Anuwum 2* + 9 X-9 X -9 2* + 9

QUESTION } [email protected] peld Determine the zeros; vertical asymplotes and end behawor ol each of the following functions Justify your Anuwum 2* + 9 X-9 X -9 2* + 9



Answers

Compute the zeros of the quadratic function. $$f(x)=2 x^{2}+9$$

This is the question that does fr X is equal to x cubed plus x square plus nine X plus name. We have to find those zeroes off their Sikh nation. So we are no factories. This e questions so we can do that. Pay for less. In the first George comes, we have to take X squared common. So when it does, I don't know. Is a Gordo X squared. Can you explain one bless 19 go X plus one. So in the next 12 times, we can they express one common. So it will be X squared plus 19 to express one x squared bless nine and to express one. So here, X squared plus nine can be the dinner as x squared minus off my history which will so well, if either they don't like this so this time can be there denies This is all the foam. Explain X squared minus a square So it could be done us expressing into x minus e. So if I do it like that, it will become physique. Wardle, Explain, Droog. Minus name and door X minus road. Mind this name Indoor X place one. Oh, I a simplified for that does would minus nine can be there than us to be in oy when I years under load minus one. So that is done. Is equal door express to the X minus two the and do X place one. So the zeros of the equation cause you don't know the equation on minus to the A plus three A. I'm minus one. So these are those off the equation X cubed plus X squared plus nine express line.

We've been asked you to find zeros of our function and then use that to help us crap. So what we're gonna do is first Rita think, what are the issues of a function in the first place? So the zeros of a function are the numbers we would have to plug in for X to get zero for. Why? So if you remember, a function is kind of like a machine. It takes things in dust, was stuck to it, and then it spit something else out. For sometimes it will even spit the same thing out, depending on what your function is. But what we need to figure out is what, specifically what Ike look in if I want to get zero. Ouch. So if we look at our function, we can see that what I look accident. I'm gonna get some number in this breath, sees it will just be something minus two that will just give me a number. And then when I would it, and over here again, I'm just gonna get some number. So this is just gonna be a number of times another number. And the thing is, I want zero in the end. I'm gonna write a musical a my first number and be my second number. If I want to multiply them to get zero. That means one of those numbers have to be zero. That's the only way you can multiply two numbers and get zero. So that means either my able zero local this one, eh? Or my B was zero. This one could be bi. One of them has to be zero or boat. So when I take a look over here, what would I have to do to make a becomes you? Well, what ex have to be for that to zero? Well, all I have to do let's say it's minus two equals zero and then find the ex. That makes that truth. So to do that, just all for that I would just add to to both sides. When I do that, get X equals two same thing or the other one. I want explosives. Mind to be zero. What would make that true? Well, I just write down experts 90 and then I find the X that will make that true. So I have two numbers that would give me that I can plug in That would give me zero afterwards. So you might be wondering. Well, just because when I look at you and just because that first number zero, it doesn't mean that the other number will be zero to, But that's okay on Lee, One of the numbers house to be zero. When I flubbed chew in this first number A become zero and the second number becomes 11. Remember, I'm just looking to and right now, but the thing is, zero times 11 will give me zero. It doesn't matter that in my second front sees it gave me a number that wasn't zero and the same thing for negative nine. Even though when I plug it into this first parentheses, it's not gonna give me zero. I'm still multiplying by zero. I get in other parentheses. So now we know what are two zeros are, and these will actually give us coordinate points. The whole point of these being called zeros is that I get zero for Why? So I have 1.20 and I have my other point. Negative mind zero. So now we're gonna rough seas. Look at you. Every 789 So here's negative 90 And here is 20 So I don't know what my graph looks like in between or arm the other sides yet, but what I do know is that my function is actually a parabola. And the reason I know that is because if I were to, uh well, this out, I know that the first thing with boiling is that I would multiply the first terms because remember, oil means start with the first in the outer and inner. And when the last specifically or multiplying by no meals like this, When I multiply those 1st 2 numbers, I'm gonna get X squared. So I know automatically. That is the highest degree I can get because I've taken all of my exes and put them together. So I know that this is gonna be a quadratic expression. So this is a problem. Correval ous look, something like this. Here's a smiley face proble, and here is a frowny face problem. The reason I called them that is because a smiley face bra villa means that we started with some positive number times expert. I'm gonna call it a and a frowny face problem means we had a negative number times X squared. So that's how I remember it. If you're positive, you're gonna smile. If you're negative, you're gonna drown. In our case, when we multiply the two exes, we get a positive number of Brock. Just positive, Invisible one. So that means our problem is a smiley face problem. So it's gonna look something like this. So this is just a vague version of what the problem looks like. If you want to get really specific, you could plug in, um, numbers in between. You could plug in negative eight of your seven and you're six all the way up to one and her ex and get the white boarding. It's out. But this is the general representation of what this probably looks like. So there we go. We know that our zeros are negative, too. I'm sorry. Positive, too. And negative. Nine. And we know that our function looks something like this when we grab it.

Okay. We have any equation or a function after back Sequels. Nine X squared minus three X minus two. And if we're gonna find the zeros of this function, all we have to do it said it to zero and solve it. Um, it would be easiest to factor our polynomial. If we can do that, we could use the quadratic formula or completing the square. Um, and I generally used the guests and check method. Um, so I know because the product has to be negative too. That really the only way is to do that are negative, too. Times positive one or positive? Two times. Negative one. Now, as I look at the first term, um, I know that I have to put two exes in there because x times x x squared. And my options are three times three is nine and nine times. One is nine. I'm gonna try three times three first. And so now I'm gonna do the foil method and make sure that this is correct. Actually, I only have to worry about the outer in the inner because I've already used my knowledge of first and last to put the terms or put the numbers, um, into my guess. So the outer is positive. Three x and the inner is negative. Six x so positive. Three x plus Negative six x. I'm gonna show you what I'm doing here. Positive three x negative six X negative, six X plus Positive three X is negative. Three x So a little bit lucky and got the correct factor the first time. So now I know. According to the zero product, property three X minus two equals zero or three X plus one equals zero. Now, I just have to solve these two linear equations. I'm gonna add two to both sides on this one, and I'm going to subtract one from both sides on this one. And so this is going to give me three X equals two, and this is going to give me three X equals negative one pretty much run out of room. But all that remains is to divide by three on both sides of the equation. So that gives us that X. The zeros are the set that includes negative 1/3 and 2/3. Okay, so there are 20

Were given a function and were asked to find its zeros. Algebraic Lee. So the function is f of X equals X over nine X squared minus four. Now, to find the zeros of dysfunction, you want to solve the equation. Zero equals X over nine X squared minus four. Now we have here is a rational equation. So to solve this rational equation, we want to factor the right hand side. But first notice that if we assume nine X squared minus four is not equal to zero, then we have that X is equal to zero. So X equals zero is one of the yeah zeros of dysfunction. Now, suppose that nine X squared minus four is equal to zero. Then we have that X squared equals for nineths or X equals plus or minus two thirds. Notice, however, that the numerator in this case is still a non zero number. So our only zero is X equals zero


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