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FTS Video for Notes: Solving Quadratic Equations

Added May 10, 2020 •

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Have paper and pencil ready to write down notes and do practice problems while writing notes. Then work on the first assignment worksheet of the week. Feel free to pause and play as you do notes and listen carefully!

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hey welcome everyone to this week's a screencast for our lessons for solving quadratic equations using all the methods this is a review from several weeks of us studying the quadratic and reviewing the solving a quadratic method so this week we're going to go ahead and focus on that remind you that we do you have a quiz depending on what day now you have your classes on Wednesday and Thursday and we will have that during or some class so if you haven't already get out of paper and pencil please follow along with the format of the notes he's mean I doing right now and then hopefully this will help you review and get you ready for the quiz and for the assignment this week we will also these nuts will also be part of that seven packet for this week as well so you do wanted to write it down for more minutes last week when we took last week we took notes considering that factoring included greatest common factor okay and then I'm going to add the magic X factoring as well as it gets and check those out there so that's how this week notes are going to be at the slightly different because we're adding on the different strategies greatest common factor is were using the gray common factor in order to solve a problem and usually when that's the case usually we are missing C from the standard form ax squared plus BX + C okay we're missing the see if you look at the example for x squared minus 2x technically there's a + 0 for the sea okay well in order for us to do this problem we're going to find the greatest common factor the greatest common factor here is going to be two acts don't forget about the two because we're X worth 4 / 2 is 2x squared / access fax and then minus the two x / 2x as one is not zero okay from here Lenny's are zero product property to X is equal to zero and then 2x - 1 is equal to zero I'm going to dip play Both Sides by to hear X is equal to zero that's one of my Solutions the equation on the right after add one and then divided by 2 So my answer here is going to be absolutely 1/2 there are two solution why are there two solutions there's two solutions because of this two 04 X Squared the power indicates how many solutions that we should be looking for at the end of it it also shows how many solutions we should have what are there rational or irrational in case it actually closer x equals 1/2 are my two solutions for this problem okay today you could always stop go back every wind in there to figure out that splint explanation or you can pause and choose to do the work yourself and then check in with this was that I provide okay so those are going to be a good thanks for the screen cast as well okay by using magic X but we can do that for problem like this we're going to solve it's going to look like x squared minus 3x minus 28 equals 0 so if I'm going to solve my magic X here my product is -28 my son is -3 okay so I'm looking at my factors of 28 go ahead and list out the factors of 28 this would be a good time to hit the pause button what the rest of the work would be the software it so if you want to press pause now and do the work that's great if you're not sure then you can continue on with me 51 * 22 * 14 4 x 7 since I'm looking at difference my product is a positive times a negative that's the only way that I'll be able to get an egg product that's why I'm looking at I know my factors when one's going to be at the + 1/2 going to be x- this is the only one that has a differences three- 7 positive for why am I using that occurs -7 time 4 is -28 but negative 7 + 4 is -3 + matches up to my son okay so I know this is the correct Factor I'm supposed to use 7 goes there in the 4% there's only one correct Factor here if you put x - 4 + x - 7 + 7 excuse me if you put positive and negative for that is not correct because of some would be positive to me so that's incorrect -7 positive for the any factor that work here so this is the only solution that works here we're not done because now that we wrote it in binomial for him we're going to use it with zero product rule again which means I want to see each other that equal to 0 I want to subtract 4 on both sides here x is equal to -4 is one of my Solutions and I'm going to add 7 to have my other solution why do I have two solutions again okay I'm going back to the original problem where does my two second power lets me know how many solutions are okay and then the one that we didn't go over last week I was actually the I guess check method can this is not on our quizzes week but I just want us to go over it because it is possible to not use a quadratic for still haven't workout especially if two solutions are fractions and not square root Solutions okay so we can do that for a problem like that 6 x squared + 13 x - 5 so if I have a problem like this will first of all I don't know 466 squared if its 1X * 6x or if it's going to be two x times 3x okay so that's why this makes it a little bit more challenging we're the reason why we would use a guess and check method is because we have a number in front of the x squared and then my product for the only two Option 1 * -5 or -1 * 5 there's only two options for my C okay so those the only two options and I'm looking at if you know how to do this then I would press pause okay that we did the factory press the pause here see if you can do the problem for the rest of you if you're not sure that we could continue to go along with the problem so I want to just for the sake of time I'm going to save time and let you know that it's 3 x + 2x okay so I tried 1X and 6s I keep trying and plug in numbers none of it was working okay let me do this problem wrong show you why it's not working okay so I'm going to do this part in Red so I'm going to do this part wrong I'm going to put positive fiber here and negative the reason why this is wrong is because 5 * 2X 10 x 3 x * -1 + -3x if I add straight down that positive 7X and that is not my middle term here I want to switch this to blue because the correct answer would be -1 + 2x + 5 so all I did was switch the second terms so this is not correct when I checked this negative 2x to have positive 15 x 3x + 5y answer it down then positive 30 minutes that's correct that is my middle term appear so as a reason I'm going to go ahead and continue with this problem by setting each of those binomials equal to zero 6 - 1 is equal to 0 + 2x + 5 is equal to 0 and add one here and then divided by 3 Texas equal to 1/3 for my question on the right I want to subtract 5 5 / 2 -5 as long as you put -2 1/2 that's okay but -2.5 that's also Okay the reason why they guess the check works for this problem is because dancers are fraction okay so there's going to be a coefficient in front of that first steps first part of the binomial for both okay so that's why this is a little bit more complicated okay I know some of you guys may know the bottoms up method if that works for you that's okay I just choose not to decide because not a mathematical way of doing things and it's not consistent with polynomial functions so I don't I don't like doing that okay or fourth strategy what's the square root strategy what do we do for sore it could be as easy as a squared minus 25 is equal to zero notice that BX is missing from Ax squared plus BX plus c because the x is missing that's how I know I'm supposed to use a squirrel strategy okay why do we start that we're going to add 25 and then we're going to score with besides Pony to that don't forget the plus-minus square root of x squared is x + -5 it could be that easy okay well let's have you guys try one x + 1 squared is equal to 49 and this is a good time to pause go ahead and pause right now for everybody and see if you couldn't do this problem on your own and then go ahead and unpausing when you are ready to answer so I'm going to square root both sides because the square root of a square don't forget my plus-minus canceled out what's 1 + - score of the 49ers seven one of those side to start isolating y or x ray I noticed when I do that the negative one goes in front of the plus-minus and then I have two solutions here again I said that earlier why do I have two solutions okay well because of that if I expand x + 1 squared I'm going to get x squared plus 2X + 1 is X to the second power again so that's why there's two solutions 7 + 30 + 81 + 7 Lottery guys are going to be more comfortable with 7 months one so I know that 6% of the easy way to calculate that my second equation -1 - 7 Baltimore negative I should end up with a bigger negative number keep the negative and just add 1 + 7 that's the correct answer that's why I P I V strategy I was completing the square completing the square or a lot of Runners I put CTS right so that's the strategy that we can call that that's you do it 4 x squared is equal to 2x - x what are you doing we haven't seen this type of okay well first of all this is not in the that we need to be so I want it in a x squared plus BX plus box warm is equal to C plus box for okay knowing that if you know how to do this okay pause button and then come back to it to check your answer afterwards okay if you're ready to check your answer all along with me I want to subtract 2X. where is -2 after now I can add the box is equal to -6 days and I add the box and what goes in the Box it's always my middle term / 2 sqrt 2 / 2 sqrt writing by the same thing on both sides. I'm adding by -2 / 2 sqrt on both sides have not changed the value of this equation is simply made it look different -2 / 2 -1 so that's where I got that -1 Square on the right side I'm going to go ahead and simplify that out which is plus one negative one squared is positive one just negative 5 just going to bring down 2x - 1 squared I think we're going to do here well we're going to do the right stuff we're going to score beside don't forget to plus minus this is x - 1 positive negative negative sort of negative I will dance we can simplify that bring about at that out as you guys know I and then I'm going to isolate access my last step picture pose in front the OnePlus reminder I go to five common questions here in Miss Rowe if we don't take out that nigg when does the incorrect and my reply to that would be yes you have to bring out the negative is I so 1 + 1 - I sqrt 2 5 is the best dancer here part of the mathematics a theme that runs I was trying to get the most simplified answer so if I left it as 1 + 4 - sqrt of -5 that's not the most simplified answer so it be incorrect okay so we wanted we do need to take out that negative and put it in I-4 I'll a strategy that we're going to go over is a quadratic formula and this is the if you're looking at any other problems. And if you're looking for well the factoring doesn't work square root doesn't work okay if that's the case I'm guessing check doesn't work that you wanted to try that that we would go straight to the quadratic formula but found it if you don't know already or if you forgot to write down the quadratic formula please and all over 2A is my quadratic formula assuming that it is in ax squared plus BX plus C form in front of my x squared is my Valley be in front of my v x x is my be Valley and then my constant is nice to have you guys do PS4 2x squared plus 8x - 15 and I-15 already lets me know that that's going to have a a possibly large number if that's okay to do this without the use of a calculator on please press the pause button and see if you can work through it upon yourself and then go ahead and unpause and Play that video on her to find out the solution so going to start by identifying my a b and c -15 okay and I'm going to start out with three squared minus 4AC cuz that's kind of easy to calculate squared - 4 * 2 * -15 please make sure you put the negative because that lets me know that negative times a negative is a positive okay that sign does matter if I instead of being a * 15 I could just do 2 * 15 which is 3030 * 4 is 120 and this is going to be one hundred I made it for so that lets me know inside the square root is going to be -1000 - sqrt of 184 which I just found / 2 * 2 PennDOT start simplifying. This isn't negative e plus and minus that down does 4 go into it yes it does Sephora goes into there are four times was that for 6/4 √ 4 is going to come out and X is equal to -8 + 1 - 2 sqrt of 46/4 t40 46 is 2 * 23 2 and 20 are both prime numbers I know I can't reduce the square root anymore but I can reduce the for eating the two I could reduce everything by 2 the cool thing about using an iPad Apple pen is that could reduce plus or minus square root of 46 all / 2 is my best answer okay so that's quadratic formula cool so oh I want to go over to scenarios okay we haven't gone over and I think the tough part about all right lessons is okay so if I had to choose your own method what strategy would I use okay well let's say I got a problem like this 3x square 5x to -8 if I see this problem I'm probably going to go with gas and check okay and if that doesn't work the strategy that I probably would want to use here that I know I'm going to get an answer is quadratic formula okay so I would probably want to use the quadratic formula strategy here you know what you do the problem because I have a number in front of x squared it's a prime number if I try to divide by 3 by everything I would have 5/3 and -8/3 of the valley by PNC does not a good option to Do complete the square OK versus if I see this x squared plus 4X I'm going to try to factor this one's not factorable I'm going to cuz the factors of 6 is 1 * 62 * 3 none of those attitude for none of them have a difference of so because I have one x squared and because my BX is an even number okay for B I would want to use complete the square and again I'm just talking to the premise of what's the easiest strategy to use okay if I had if I knew how to do them all well well here the complete us prep squish out of your be the fastest and easiest method to talk down question can I use quadratic formula for this problem absolutely okay so you can do that but on the quiz I'm going to ask you to specifically using a specific strategy so that has to work has to be there and then I would almost have enough problems where you get to choose your own that are okay so you have to know about new all the strategies and you have to know how to tackle problems from the very beginning which is the choose your strategy in to do in versus I gave you the strategy and you have to do it like factoring square root complete the square quadratic formula okay to put her notes for screen if you want to go ahead and sell those after practice that's great I'm not going to go over there solutions for those but I'd imagine with all the practice and we just did that you should be able to get to it or you could compare your notes or answers were pass me that be great as well see if you guys both did it correctly is the conclusion of a note I'm going to you should go ahead and download or view the worksheet for your class and go ahead and work on that and then I'll see you in class on Wednesday and Thursday they don't forget to keep the set of notes as you will turn it in this weekend I'll tell you on Wednesday what to turn in for Thursday if I seen on Thursday's class until what you're supposed to turn in my Friday okay alright have a good day

Uploaded by Daniel Rho.

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FTS Video for Notes: Solving Quadratic Equations

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