Hello, hello, hello. This is Miss Bzinski, your algebra 2 teacher for advanced algebra 2. And this is a quick review uh of how to pass ACP for semester 2, going over all of the uh TEICSS, which are on your ACP blueprint for semester 2, advanced algebra 2. All right, so let's make sure we believe in ourselves. Make sure you pause the video. Right now you should be pausing the video and put on a split screen uh the calculator the TI3 calculator which you can get in Google Classroom and put it on a split screen with the video on one side and the you should have the calculator on the other side and then you can pause the video see if you can get the answer and then play the video and see if you have the answer. Okay, so let's go ahead and look at the first question. If f ofx= log base 2 of x + 4 - 8, what is the inverse? When you see this little negative one, they are talking about an inverse function. Step one, to find an inverse, you have to switch the x and y. This is your x and f ofx is your y. So on your scratch paper, you would write y = log base 2 of x + 4 minus 8 when you see this on your screen for the ACP. And step one, you're going to take the x and y and you're going to switch them. So you would have x = log base 2 of y + 4 - 8. And then after you switch the x and y, um, you've got to move whatever's on the outside. So there's a minus 8 on the outside that's going to have to move to the other side. The opposite of subtracting eight is adding eight. So your next line's going to be x + 8. That's how you're going to move that equals log base 2 of y + 4. So after you switch the x and y, you move the stuff on the outside. Then you have to change forms. Uh so this is when you're going to click your heels and say the log is the exponent. So the log is the exponent. This is your exponent and this is your base. So that little two is now going to become a big two. And this is your exponent. It's going to become very small and raised up. And then this is what's left over. And the last step is to isolate the y. How do you isolate the y? Well, the opposite of adding four is subtracting four. And this is your inverse, which is commonly written f -1x, which is pronounced the inverse of f ofx. All right. Uh, if you got that one, great. You should be getting this one right. So, remember, recap. When you find inverses, switch the x and y. Move the stuff on the outside. Change forms because you're going to see it's multiple choice. There won't be any choice with the log. Everything's going to be exponential. And then after you change forms, isolate the y. All right. Next question to review is going to be 2 a 2 c. Um, if the domain of this function uh is restricted from 3 to infinity, you're going to graph the inverse. Okay. So, how do you do that? Well, first you have to find the inverse. So again on your scratch paper you would write y = x - 3^2 + 5. Go ahead and freeze frame the uh video. See if you can get this answer without um looking at my solution and then come on back and check out the solution. So I'm going to switch the x and y. So that's going to be x = y - 3^ 2ar + 5. Then remember you have to move the stuff on the outside. So the opposite of adding five is subtracting five. And you're trying to get this y isolated. So the furthest one would be the square. And the way you get rid of a square is plus or minus the square root. So your next line you would have plus or minus the square t of x - 5 = y - 3. And then you're going to isolate the y. So subtracting three is adding three. Okay? So you're going to they're normally going to add the three in the front. It's okay to put it in the back, but on multiple choice they're going to put it in the front. So that this minus three is going to become a positive three and they'll put it in the front. And then you just have to decide which branch do you want. So that is your inverse. Um since they're restricting it from 3 to infinity, those are positive numbers. You want the positive branch. So the one you want is 3 + the<unk> x - 5. and that's the one you want to graph. So, how do you graph that? You go on your calculator to y equal and you're going to type in 3 plus square root is right here. It's yellow. So, second square root of x - 5 and close the parenthesy. And then you can hit zoom six. That's a 10 x 10 screen. And you're looking for that graph. Now remember this is a hoe and hoes are opposite of what you think. So you think the hoe went left but it really went right five and this goes up three. So right five up three. That's the graph you're looking for. All right, moving on. Next topic is 2 a4f. We have to solve um a square root uh equation. And again, how do you solve equations? You always move the one that's farthest from the x but still on the same side of the equal side. So you have a right side and a left side. So who's farthest from the x? It would be this plus three. And the opposite of adding three would be subtracting three. So that's the first thing you're going to do is move that three over. So then your next line is going to be -2<unk> of 3x - 4. And you could type this in your calculator. You would type -6 - 3. Or you could use your head. I owe somebody $6. I owe somebody $3. That means I owe somebody $9. And then who do I move? Uh the one that's farthest now is anything on the outside of the house which read this -2. Now when you're next to something that means multiply and the opposite of multiplying is dividing. So you're going to divide by -2. Do not change this -2. You're doing the opposite of multiplication. The opposite of multiplication is division. Um so that's how you move that. Now um you could type this in your calculator or you could leave it. Uh now I have to get off the square root. So I have square<unk> of 3x - 4 =9 over -2. And the way I get rid of a square root is I have to square it. That's how I'm going to get rid of it. I square it. And then these will cancel out. So then I'm left with 3x - 4 =9 / -2 squared. And now I'm going to isolate that x. I'm going to move the four over first. The opposite of subtracting four is adding four. That's how I'll move the four over. And the way I'm going to move the three is to divide. And that's my answer. Now, you have to be careful about typing this in your calculator. You cannot type it like this. Um the calculator doesn't know you want all this to stay together. So, you're going to need a a parenthesy on this entire numerator uh in addition to this fraction. You don't need one on the denominator because there's only one thing here. Um you could put it, but you don't need it. And you don't need one on the whole fraction because you're not adding it to another fraction. you're not subtracting or multiplying or dividing to another fraction. So, the correct punch I would do this on home screen second quit would be open the numerator, open the fraction, and then you're going to type -9, that's the white key, uh divided by uh -2, that's the white key, close the fraction, square the fraction, + 4, and then you want to close the numerator and then divide by three. Um, and there's your answer. Now, they're not going to have an answer like that. They'll have a fraction answer. So, you can change it to a fraction by hitting math. Fraction is number one, and press enter. So, they'll have 97 over 12 as the answer. Now, if you forget how to convert things to fractions, you can look at the choices and just type the choices in. So, you could type 97 / 12 and then you can match that to your decimal if you forget that the fraction key is under the math key. All right, moving on. Next question we have to do is um from topic 2 a 5A. We have to describe transformations. There's going to be an awful lot of questions about transformations. So this minus five in the back is going to move it down five. Uh plus is up, minus is down. This is a hoe. Hoes are opposite of what you think. Hoes are horizontal. They can only go right or left. You think the hoe went right, but the hoe really went left. So it's going down five, left four, and then when the number in front is less than one, and 1/2 is less than one, it's 0.5. When the number in front is less than one, that's called a vertical compression. When it's more than one, it's a vertical stretch. Now, what if you had something like this, -3 f of -x - 4 + 6. The plus six is going to move it up six. Um, this is a hoe. Uh, and this right here is a reflection over the y- axis. This negative would reflect over the x-axis. And the three would be a vertical stretch. All right. Next topic. You're going to have to be able to change forms from uh exponential. This is exponential because x is the exponent. And you've got to change it to logarithmic form. That's our next topic. So, how do you change this into logarithmic form? This is when you're going to click your heels and remember that the log is the exponent. The log is the exponent. This right here is your exponent. Now, they're not going to use log. All the choices are going to have ln uh because you have a base of e. So, whenever you have a base of e, you're going to use natural log. So, the log is the exponent. The exponent is 3x + 2. And then over here down below should be your base. If this is your exponent, it is attached to your base. So, your base will be an e, which they will not write. They expect you to know it's there. And then what goes here is what's left over, which is this six. So, the answer you're going to see is natural log of 6 = 3x. Oops, I didn't write this right. Let me write it again. Nicer. The answer you should see is ln 6= 3x + 2. Sorry, I miswrote that. That would be the answer you would see. You're not going to see this base of e. That's an imaginary e. They will not write it. Okay. Next question topic is going to be 5d. You have to be able to solve logarithmic equations. And we're going to round our answer to the nearest tenth. All right. Step one, you're going to take two logs and change it into one log. You can do that by looking on your formula chart, which is on your desk. Um, this is this formula right here for logs. If you have two logs, you can change them into one log. Addition becomes multiplication. Subtraction becomes division. So, this one has an addition problem. So, the addition will turn into multiplication. So, I'm going to have log base, sorry, base two. And then I'm going to take this and this and multiply them. Addition turns into multiplication. So, I'm going to have x + 4 * 3x = 6. So, two logs became one log. And now I'm going to have to get the log to disappear. The only way to do that is to click my heels and change forms, change it back into exponentials. So, we say the log is the exponent. This is your exponent and this is your base. So, that little two now is going to become a big two and the exponent is six. And what's over here is whatever's left over, which is x + 4 * 3x. And now we have to solve this. Um, the easiest way to solve this is to use your calculator. But if you want to use your calculator, you're going to need to send this to the other side. So the opposite of a positive will be a negative. So you'd have subtract 2 ^ 6, which would make this side equal to zero. And then what you would use is solver. Um, you can't use solver unless your equation is set equal to zero. Where is solver? A solver is in the math key and it's at the very bottom. So solver is at the very bottom. There it is. So solvers in the math key. It's math zero. Um so math zero is your solver key. And then what you're going to do is type this in. So you're going to type uh open parenthesy x + 4 close parenthesy open parenthesy 3x close parenthesy - 2 power of 6. So you just type it in, press enter, and now it wants you to do a guess number. So, so I'm going to guess 100 and it'll find the answer closest to 100. How do I get the answer? I hit alpha solve, which is green button, enter. That's where your solve key is. And it's telling me one of my answers. Well, I do want it to the nearest tenth. So, this is 10th's place right here. So, I look to the right. The three means I'm going to keep it. So, it' be 3.0. So, I know that one of my answers would be 3.0. How do I get the other answer? I put in like negative 100 and then alpha solve. So my other answer to the nearest 10th would be -7.0. Now you're going to have to eliminate the negative answer because we do not take logs of negative numbers. Even though these are solutions to this equation, uh only the positive one is the solution to this one. Uh so be careful about that. Never uh do the um negative numbers for log. It's not in their domain. All right, I'm going to get out of here. Second quit and move on to the next topic. Our next topic is 6B, which is how to solve rational equations that are rational fractional exponents, which is what we have right here. So, we're going to try to get this x isolated. So, who is farthest? You always move who's outside of the house, then you move the house, and then you can get inside of the house. So, who's outside of the house? The two. You're going to have to move this two. When you're next to something, that means multiply. So, the opposite of multiplying is dividing. That would be step one. Make sure you are freeze framing this video and practicing on your own paper and with the calculator on a split screen and then you can hit play and see if you're if you have your solution correct. Uh watching me is not going to help you. You have to do it without looking at how I solve it. If you have to keep looking at my solution steps, you're not ready for the test. 16id two is eight. So now who's farthest? Now you have to move the house. The house is this 1/3. So, how do you move that? You have to flip it. Use the reciprocal. So, the reciprocal or if you flip 1/3, you get 3 over 1. If you do it on the left, you do it on the right. These will cancel to one, which is what I want because I'm getting it at 3 over 3, which is just one. So, next line, I will have 4x - 1. And then I'm going to do 8 to the^ of 3 because 3 / 1 is just three. So, I'm going to get out of here. Make sure I'm on the home screen. That's where you do computations. And I'm going to do 8 power of three. So if I do eight power of three, I'm getting 512. And then I'm going to move the one farthest, which would be this uh minus one. Opposite of subtracting one would be adding one. So now I have 4x = 513. And then I have to move this four. When you're next to something, that means multiply. And the opposite of multiplying is dividing. So that's how you're going to get it. And then you just type it in your calculator. 513 / 4. and your calculator gives you the answer is 128.25. Next topic is uh 6 I and in this topic you have to be able to uh solve um addition, subtraction, multiplication with with rational with fractions uh equations. So this one they want the value of x. That means these are the values of x. So what you want to do is store these in x. one of these works. So, you just store it in x. So, how do you store it in x? You're going to hit clear on your home screen and you're going to take like uh -4 and then you're going to store it in x and press enter. So, now the calculator remembers that x is4. And then you're going to type this in your calculator on the home screen. So, you're going to type open o. You need lots of parentheses. I would recommend you write this down when you're taking the ACP on your scratch paper. And then make sure you put parentheses on the numerator and parentheses on the denominator. In addition, you're going to need them around the fractions if you're adding or subtracting or multiplying and dividing. And we are. So, we're going to need one on this fraction and one on this fraction because we have a fraction plus another fraction. We won't need one on this one because even though it's a fraction, we're not adding it to something or multiplying or subtracting or dividing. You could put it. It's not wrong. You just don't need it. All right. So then you're going to type what you see. So I have uh I'm going to open the fraction. Then I'm going to open the numerator. Then I'm going to type the numerator. 2x^2. Sure I'm typing this right? Yes. Okay. Then I'm going to close the numerator. Then divided by open the denominator. x - 4. Close the denominator and close the fraction. Then I'm going to put this plus sign in. Then I'm going to open the next fraction. Open the numerator. Type in the numerator 19x. Close the numerator. Then divided by uh open the denominator x^2 minus that's the blue key 16. Close the denominator and close the fraction. Press enter. Now I'm getting an error message. Why am I getting an error message? Well, I tried to use -4. And if I put a -4 right here, I would get -4^ squared. And4 *4 is positive 16. And 16 - 16 is 0. You're not allowed to divide by 0. Um, so that's why this is giving an error message, which means this is not the right answer. So I'm going to get out of here. Second, quit. And I'm going to hit clear. And I'm going to try the next one. So I'm going to store in a negative three halves. So I'm going to go negative. That's the white key. Three. So I make that clear -3 / 2 and I'm going to store that in x and press enter. And then I'm not going to retype this because it takes too long. So we can call back the history of our calculator by hitting the second key and enter. It calls back the last thing the calculator did. And I don't want that one. So go back in the history again. Second enter. And that's the one I want. So I don't have to retype it. And I'm gonna go ahead and press enter. Now, how do I know if that's right? I'm going to have to type the other side of the equal sign. So, I'm going to type open numerator 7x - 3x^2 close the numerator divided by open parenthesy open the denominator uh x^2 - 16 and close that denominator. And I can see that the left side was 1.25 and the right side is 1.25. They are matching. they are equal. That means I have a winner. The correct answer is choice B. Now, the reason I'm not going to try zero is because I know zero works. It's in every answer choice. So, I know I don't have to even store zero. Zero will work. Um, but neg3 choice B is your answer. All right, I'm going to get out of here. So, I'm going to hit clear. I'm done with that problem. And our next topic, Whoa, whoa, whoa. Got a lot of topics today. All right. Uh next topic is topic 6L 2 A6L which is uh inverse variation. Uh the key word of course is varies inversely. You will see that twice on the ACP. Um so how do we do it? Well the first thing it uh go ahead and hit pause and see if you can work this out and then once you've worked it out then hit play and see if your solution matches mine. So it starts with X. You start with X. Varies inversely means you're going to have to invert. Invert means flip it. What are you inverting? This y. So this y goes down here. And what goes up here is called k. It's a constant. It's a number that we have to figure out. How do we figure out the k? We plug in what they give us. They tell us that x is 6. And they tell us that y is 32. So we plug those in and we get 6= k / 32. Now, how do I isolate the k? Well, the opposite of dividing by 32 is, of course, to multiply by 32. And then you can use your calculator if you're not sure and you can just type in 32 * 6 and your calculator is going to tell you that that's a 192. So 192 is your k. Then you're going to take this and put it back where the k is. So now you have x= 192 / y. Don't use these uh numbers more than once. They were only given to you to find the k. Once you find the K, you don't use them again. Now, there one of the varies inversely. Uh, this is the answer. They just want you to get the equation that models it. But then there's another one that says varies inversely like this where they want you to keep going and make a prediction. They want you to know what is the value of x when y is three. So you have to keep going and put that three where you see a y. So you're getting x= 192 / 3. And you could type that in your calculator very easily by typing 192 / 3 and your calculator gives you the answer of 64. The answer to this problem is 64. All right. Next topic is 7b. You have to know how to multiply um polomials. How do you multiply polomials? It is multiplication because you have a parenthesy next to a parenthesy. So what you're gonna do is not look at this negative -2. You're going to take this 4x and you're going to multiply it with everybody over here. That's what you're going to do. So, what's 4x * x^2? That would be 4x cubed. What's 4x * -3x? You could use your calculator if you needed to type 4 * -3. Your calculator will tell you that's -12. And x * x would give you an x^2. Then you have 4x * pos1. That would be a positive 4x. So, you're done distributing and multiplying with the 4x. So, now you're going to cover up the 4x and you're going to do the same thing with this -2. You're going to take this -2 and multiply it with everybody over here. So, what's -2 * x^2? That would be -2x^2. And then you're going to have -2 * -3x. A negative * a negative is a positive. So, we get pos6 x. And then -2 * pos1 is -2. And now we're done multiplying. All you have to do is combine like terms. So this is my only x cubed. So the final answer will start 4x cubed. Now I'm going to look for my x squares. Um this is an x squar and this is an x squ. So I have to combine like terms. I'm no longer multiplying. I'm either adding or subtracting. So this would mean uh if you want to type it in a calculator, you would type -12. That's the white key minus 2. And or you could use your brain and say, well, if I owe somebody 12 and I owe somebody two, I must owe a total of 14 of these. And then you got to do your xylophones. So I see that I have four xylophones and I have six xylophones. So that means I must have 10 xylophones. And this minus two is going to just come down. It has no one to combine with. And that's the answer. Easy breezy. Just make sure you're multiplying with everybody. Use your calculator if you need to. All right. Next topic is 7 C. You have to be able to find the quotient of polomials. Okay. So, how do you find the quotient? The quotient means the answer to a division problem. So, if you divide this, they're saying one of these is your answer. That means this must equal one of these. Um, so how do you do that? The easiest way would be to put all of this in your calculator in Y1. And then you can put one of these in Y 2 and then see if these are equal. How could you see if they're equal? You can go to the table. And in the table, you're trying to see if the Y1 is exactly the same as the Y 2. All right, ignoring any error messages. All right, so here's what I'm going to do. Go up here to Y equal, hit clear, and I'm going to type this in. So I'm going to type open parenthesy 3x power up 4 plus x our cube key is math 3 or you can do power up 3 + 4x^2 or you can do power up two plus 2x - 4 close parenthesy. Then we're going to hit divided by that's this blue key. And then we're going to open parenthesy x^2ar + 2 and close parenthesy. Then you're going to come down and put in an answer choice like the first one is 3x^2 - x + 2. And then go to your table, second table, and you're looking at the y1 and the y2. And you can see these are not the same. -2 is not the same as positive2. So the answer is not choice a. So, go back to y equal. Arrow down to y 2. Clear it out. Try the next one. 3 x^2 + x - 2. Then let's go to our table. Second table. And we're looking at our y1 and y2 column. I'm seeing -2, -2, positive2, positive2, 12, 12. This is what uh it looks like when they're equivalent, when they're the same. So that is our answer. The answer is choice B. Okay, let's move on to our next topic. Our next topic, you have to be able to find a factor. Uh there'll be two questions about finding a factor. Uh what's the easiest way to find a factor? Well, you're going to take this and put it in y1. You're going to take this and put it in y 2, but you're not going to go to the table because these are not going to be the same. What you're trying to do is you're going to get some kind of graph. And these graphs have x intercepts or zeros. You want to make sure that this line, which is y= mx plus b, goes through either this zero or this zero or this zero. That's what a factor looks like. This is not a factor. This is not a factor. This is a factor. So it just has to go through that zero somehow. Uh then it's a factor. Okay. So I'm going to go up here to y equal. Clear out everything. I'm going to put in what they gave me, which was 9 x. The cube key is in math three, or you can do power up three. Minus is your blue key, 18 x²ar minus is your blue key, 16x + 32. Then I go down and put in one of the choices. 2x + 5. And I'm going to go and look at the graph. How do I look at the graph? Zoom 6 10 by 10. So here we go and here comes the line and I can see this line is not a factor because this line is not going through this zero or this zero or this zero. That's too high. It's not not where it's supposed to be. So that's not a winner. So I go back to y equal. I arrow down. Clear. I try the next one. 3x minus 4. Then I'm gonna hit zoom six. And here's my function, my cubic function. And here comes my linear factor. And I can see this one is a factor. Now, if it's hard to see it on Zoom 6, you can do a smaller screen, which is actually zoom 4. Zoom 4 is a 4x3 window. Zoom 6 is a 10x10. So, um, I'm making a smaller window, and I think you can see it better now. Can you see that it is crossing? Okay. Oops. Sorry. All right. So that one is the winner. That one is the factor. All right, let's go to the next question. Next topic is 7E. And that topic is how to do a complete factorization. Your key word there is complete. In order to have a complete factorization, you're going to need a long answer. So you want to get rid of the ones that are not long. So you would get rid of choice A, you get rid of choice C. Uh, if I'm going to completely clean your house, it's going to take me a long time to clean everything. So, complete does mean it's going to be a long answer. So, what you're going to do is put this in Y1. You're going to put one of these in Y 2 and see if they're equivalent. And you do that by looking at the table. So, I'm going to do that for you right now. I'm going to go up here to y equal. I'm going to clear out what I have. I'm going to type in what they gave me. 2x math 3 - 3x^2 - 32x + 48. Then I'm going to come down here and I'm going to put in one of these long ones. So open parenthesy uh 2x u - 3 close parenthesy open parenthesy x - 4 close parenthesy open parenthesy x + 4. Okay. And now I'm going to look at the table. Second table. And of course I'm looking at my y1's and my y twos. I have a 48 and a 48. I have a 15 and a 15. I have a -12 and -12. This is a match. This is the complete factorization. Okay. I have a match. Next topic is 7F. You're going to have to be able to multiply uh fractions with polomials with um rational. You have to have fractions and be able to multiply them. That little dot means multiply. And you're going to have to figure out which one's equivalent. Equivalent means they have to match up. So I could take this and put it in Y1. I could take these answers and put them in Y 2 and go to the table to see if they're equivalent. The table will always tell you if things are equivalent. You're going to use the table for quotient. You're going to use the table for equivalent and complete factorization. All right. So I would write this down on your scratch paper. And don't forget to put a parenthesy on the numerator, parenthesy on the fraction because you're taking a fraction and multiplying it by another fraction. Anytime you're going to take a fraction and multiply it, add it, subtract it, or divide it, you need to hug that fraction. All right, so let's go ahead and type that in. So I'm going to go up here to y equal, clear out what I have, and I'm going to type this one in. So, how do I type it? I'm going to go open the fraction, open the numerator, type the numerator, x^2 - 4, close the numerator, divided by open the denominator, 2x^2 - 5x + 2. Close the denominator and close the fraction. Then I need this multiplication, which is right here. Looks like a little star. Then I'm going to open the next fraction. Then I'm going to open that numerator. I'm going to type the numerator. 4x^2 - 1. Close the numerator divided by open the denominator and then type the denominator. Make sure you're hitting that - 3x - 2. Close the denominator and close the fraction. Okay. Then you want to arrow down. Uh you could try the first one, which is -1. And you can go to the table and see if the y1's and y2s match. Um they don't. That's a five and that's a negative one. That's not what a match looks like. You could try the next one. Arrow down and you could put in a positive one. Go to the table and you can see these do not match. I get a negative 1 and a positive one. That's not a match. So I'm going to go back to y equal. Arrow down. Hit clear. In order to type this, you're going to need a parenthesy on the numerator and a parenthesy on the denominator. You don't need one on the fraction because you're not adding it or multiplying or dividing it with anything or subtracting it. So, it's just open the numerator x minus 2 close the numerator divided by open the denominator x + 2 close the denominator. Then go over to the table second table and you can see these uh that one looks good but this doesn't look good. This one's -3 and this is.3333. That's not a match. That's not what it looks like. So, if it's not A, B, or C, it must have been D. But I highly recommend that you type it because there is a chance you could have made a mistake. Um, so I'm going to type the last one. Open parenthesy for the numerator. I'll type in x + 2. Then I'm going to close the numerator divided by open the denominator xus 2 and close the denominator. Then I go to my table and I should see a match. 1g1 beautiful -3g3. Excellent. All of these are matching. This is what equivalent looks like. Correct answer was choice D. Next topic is you have to be able to simplify square roots, okay, with radicals. So, how do you do that? You're going to have to um create what's called a factor tree. And you got to figure out how to multiply to get 72. There's a lot of ways you could do 9* 8 or if you're like having a brain for it and you just can't figure it out, take your calculator. The opposite of multiplying is dividing. So, you could try dividing by two. And guess what? It works. So you could start off with 2 * 36 because if you divide this, you get 36. Which means if you multiply these, you get 72. So you could start with 2 * what? 36. And then you could take 36 and you could also divide that by two. There's a lot of ways to do this. 36id 2 is uh 18. So you have 2 * 18. And then 18 is 2 * 9. And 9 is 3 * 3. And then once you're done factoring it, you look at the bottom of the factor tree. Don't look at the 36 because there's a branch. You look at these. These are your apples. They're at the end of the branches. And you're looking for happy couples. So I see a a couple a pair of twos. So I'm going to pull it out. These are gone. I don't see a pair here, but I do see a pair of threes. So I'm going to pull it out. But this is lonely. There's no match for this one. So that one has to stay in. So, this two has to stay inside the house, but these couples came out. And what do you do with the couples that come out? You multiply them. 2 * 3 is six. So, you're looking for an answer with a six on the outside and a two on the inside of the square root. Now, we're going to do the same thing to the x ^ 13. x ^ 13 means x * x * x * x * x * x. When you get really good at this, you really won't have to do all this. 1 2 3 4 5 6 7 8 9 10 11 12. And I need one more. 13. Okay, so I've got 13 of my X's. And I'm looking for couples. I see a couple here. That's going to come out. I see another pair. Another couple. It comes out. Another couple. It comes out. I see another couple. It comes out. I see another couple. It comes out. I see another couple. It comes out, but this one's lonely. And lonely people have to stay inside. They don't get to party on the outside. So, this one's lonely. It's got to stay inside. So, what do you do with all these couples that came out? You multiply them. So, what's x * x * x * x * x * x? 1 2 3 4 5 6. So, it' be x to the power of six. And then you do the same thing with the y's. So, this is y to the 15th. Um, that is an awful lot of y's. That's 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15. And I'm looking for couples. I see a couple there. It comes out. I see a couple here. It comes out. I see another couple right here. That couple's going to come out. All the happy couples get to party outside. This couple comes out. This couple comes out. This couple comes out. And this couple comes out. But this one's lonely. And lonely single people have to stay inside the square root. They don't get to come out. So all the ones that come out, they're going to get to multiply. So that would be 1 2 3 4 5 6 7. So you're gonna have y to the^ of 7. So what I'm getting is 6 x to 6 y to the 7th square<unk> of 2x y. But they are going to drop an absolute value because this is an odd exponent. And the reason they're dropping it, you're going to see that in answer choices, is because we can't have negatives under square roots. You can't take the square root of anything negative. So all of these came from inside. So it's okay to have a power of six. That's always going to produce a positive number. But a power of seven could produce a positive number or a negative number. The absolute value is ensuring that whatever it is, it'll always be positive. So that's the answer. Uh that would be correct. All right. Next topic is 7h. You do have to be able to solve these rational fractional exponent problems. Uh, we're going to round our answer to the nearest 10th. All right, so we're going to solve this for x. So, who would move first? U, well, I would move the one farthest away. Who is farthest from here? It would be this minus two. Opposite subtracting two would be adding two. Please make sure you pause the video. See if you can do it without looking at my solution. Get the calculator on a split screen. So, now you have 4x to the 34s = 50 + 2 is 52. So now, who's farthest? It would be the four. Uh, not the three force. The 3/4 is the exponent. Exponents are attached to a base. When you're attached to something, you are extremely close. This one is next to it. It is close, but not as close as being attached. So, the attached one is going to go last. This one's going to go first. It's the farthest one. So, how do you move that four? When you're next to something, it means multiply. So the opposite of multiplying would be dividing. So then you have x to the 34s. If you don't know 52 / 4, um you can turn your calculator and just type it in 52 / 4 and your calculator is going to tell you that that's 13. And now you're almost done. All you have to do is move this fraction. How do you move fractions? You have to do the reciprocal. Um which is also some people say flip it. You got to flip it. So, if you flip 3/4s, you're going to get 4/3. But if you flip the right side, you have to flip the left side. 3 * 4 is 12. 4 * 3 is 12. And 12 / 12 is 1. That's what I want, an imaginary one. But to type this, you're going to have to type 13 power up open parenthesy 4 / 3. You are going to have to hug this fraction to tell the calculator you want to keep that together. And you're going to do all that on your home screen. So, here's my home screen. So, I'm going to type 13. Did I type 13? Nope, I didn't. Let me try again. 13. Uh, power up open parenthesy 4 / 3. And now you're telling the calculator to keep that fraction as an exponent. So, this is my answer I'm getting. And I do want it to the nearest 10th. So, I can see the five is in the tenth's place. So the tenth's place, let me pull it up so you can see it, is right here. If I look to the right, the six is telling me to bump it up. So to the nearest tenth, the answer would be 30.6. You have to bump this up. This answer would be 30.6. All right. Uh we're almost done. I think we've got two more questions. Yay. All right. Um we do have you're going to have two rational ones that you have to solve. Um, this one's a little bit different, but not hard. Um, again, you move the one that's farthest. Who is farthest? It would be this plus one. You always move outside of the house, then you move the house, then you can get inside the house. So, what's the opposite of adding one? It would be subtracting one. So, next line, you would have open parenthesy 3x - 2 to the 1/3 and 5 - 1 is four. And now you're going to have to move who's farthest. It would be this fraction, this house. How do you move the fractions? you flip them. If you flip 1 over 3, you're going to get 3 over 1. Um, so these will cancel out and now you have 3x - 2 and 3 / 1 is just 3. So you can type in your calculator four uh math 3. And your calculator tell you that you take four and power it up to three, you're going to get 64. And then you're going to move the one farthest. And the one farthest would be this minus two. And the opposite of subtracting two would be adding to. So now I have 3x = 64 + 2 is 66. And then I have to move the three. Uh when you're next to something, that always means to multiply. And the opposite of multiplication is division. So if you're not sure, you can always use your calculator. Please use your calculator. 66 / 3. Humans make mistakes. Calculators don't. Unless you type it wrong. So you can see that 66id 3 is 22. And the answer to this problem is 22. All right, my last review problem. Um, you're going to have four tables. Okay, we're going to talk about these tables and how to do these tables. So, um, what I want you to do right now is to freeze frame the video. You should be doing that after each one of these questions. See if you can get this answer and then come on back and check your answer. Go ahead and pause it and work it out. All right, so there going to be four tables on this test. They told us there's going to be four tables. Step one, when you have tables, don't go to this table key. This table key only works if you go to Y equal. All these blue buttons go together. When you when they give you a table, you have to go to the stat key because it's statistical data. Go to edit and if there's stuff there, it's up, clear, down, up, clear, down. So, you're going to put in -1, enter, zero, enter, one, enter, two, enter. You're going to arrow to the right and put in uh your y-coordinates in list two.5, enter, 4, enter, 32, enter, and 256, enter. All right. The problem with this is they're not telling me what kind of data this is. And there's three types of datas you have to know for your ACP. And the three are you have to know how to do linear, quadratic, and exponential. And that's it. Those are the only three they can ask. So in order to figure out which one you should use, you're going to need to turn your diagnostics on. So you want to go second zero so you can get into this catalog key. But catalog is yellow. So it's second zero to get into the catalog. And then you're gonna have to arrow down till you get to A B C D. Here comes the D's. And then when you get to the D's, you're looking for this one called diagnostics on. Once you find it, press enter. Now all that does is select it. Go ahead and press enter one more time and it turns it on. Now once you turn your diagnostics on, it's going to stay on unless you reset your calculator. Now I can figure out which one I should be using. So I go back to the stat key, go over to calc and I try linear. Linear is number four. Okay. So when I do linear, I am looking for the R squar. Remember you're in algebra 2, you're looking for R2 R 2. So my R squar I can see is 698. Uh which is like almost 70% 69%. Um now I'm going to go to quadratic. Quadratic is quad. That's how they abbreviate it. And I'm going to be looking for the R squar. So go back to stat calc. Linear is four, quadratic is five. I'm going to press number five and press enter. And again, I'm looking for the R squar, which is at the very bottom, 967, which is stronger. If you have a 96, that's stronger than getting a 69. And the last one I have to do is exponential. And I have to look for that R squar. So I'm going to go stat calc. Now exponential, you don't see it. If you have it memorized, great. If not, you can go hunting. It's the one that's uh expands for exponential and it is stat it is uh stat cal zero. Press enter. And I can see on this one my R squar is 1. So this is like saying 69%. This is like saying 96%. But this is like saying 100%. When you get an R square of 1, it's a perfect fit. It means it's the winner and you don't have to do anything else. It's a perfect fit. So, I know that my equation is y= a * b to the power of x. And they're giving me the a and they're giving me the b. All I'm going to do is plug in the a and the b. So, I'm going to write down that equation. So, that equation would be y equ= my a is 4 times what's my base? My base is going to be eight. and then I have to power it up to x. So I get this equation from the top line. And now I'm going to use that equation um to get a prediction. Um so how do I do that? I'm going to find x if y is48. So I have to put the8 where I see the y. It's got to go where the y is. Okay. Um, so I would have 248 = 4 * 8 to the^ of x. And I got to figure out what x is going to make this true. Now um it's going to be multiple choice which means they'll have answers like um let's see like like five 4 3 2 they'll have answers. Okay. So all you have to do is take these answers which are x's and plug them in where you see an x. I could put a five there, a four there, a three there, and a two there until I can get the one that gives me um 248. So, if I try a five, uh I'm going to press 4 * 8 power up five. Did it work? No, I didn't get that. So, the five doesn't work. So, now I'm going to try the next one. Uh, I'm going to go second enter, call it up, and change the five to a four. Nope. I'm going to go second enter, call it up again. I'm going to change that four to a three. Did it work? Yep. I got a winner. So, when I plug in a three for x, I am getting 248. So, the answer is choice C. Now, on some of the um table problems, you don't have to do this. You just have to write the equation and you're done. Some of them you have to do a prediction. Um, and some of them you need the diagnostics on. Now, if all of the choices look like y= mx plusb, you don't need your diagnostics. That's linear. If they all have x^2, x^2, x^2, you don't need your diagnostics on. It's going to be quadratic. If they all have x as the exponent there, you have to do stat calc zero for exponential. And that concludes my review. I wish you the best of luck. Uh, make sure you believe in yourself. Make sure you study. Make sure you pause my video. And I look forward to seeing you next school year. Bye-bye. Go Jacks. Don't forget to click your heels. The log is the exponent.