FUNÇÃO QUADRÁTICA | FUNÇÂO DO SEGUNDO 2º GRAU - AULA 1

The quadratic function or polynomial function of the 2nd degree depends on the material bringing you different names, but you must be thinking where does it say that I'm going to use it in my day to day ? Folks Did you know that the quadratic function has a strong relationship with the economy because it determines the profit, cost and expense functions, so be sure to watch Gis's class to understand the essence of the 2nd degree function and crush your activities and already take the opportunity to subscribe to the Gis channel and leave your like for the 2nd degree function class or quadratic function, but let me ask: have you watched all the classes on 1st degree function or function? I'll leave it here in the description, back in the description there are links to all the classes related to the function of the first degree because it is possible that if you are in the quadratic function you have already studied the function of the first degree, okay.

So what is a quadratic function? It's every function whose law of formation it can be indicated by look here fdx ok when we make a contextualized situation we change this FD function for the name of the context for example I'm talking about the look and I could change f for 1 because then a company's profit would depend on the amount of sales that the company made, so I could change the f here for the context being analyzed in the question. So let's talk in general, first of all, then f of x = ax squared + BX + C And here, then, as is our law of formation of the 2nd degree function, you can see that we have the coefficients ab and c, there is something familiar to you here right a quadratic equation here look Air is that guy who is on the x squared side Bea is the guy who is on the X side and you are alone so I can identify the coefficients within the second degree function AB and C Hi guys already marked but then you have to observe something the ABC coefficient they belong to the set of real numbers and people ar can never be zero it has to be different from zero Why does it have to be different from zero what can this guy imagine that 00 x that they gave there if he does this first part it is not for high school But how am I going to identify looking at all these here for example that I put how I identify if it is a function of high school or not That's why I say back to the previous class because when I talk about a function I'm going to talk about dependent variable independent variable and all this explanation I did when I spoke about the function of the first degree because you remember, right, the mathematics content is a content continue I need for me to be in this content I need to go through the previous ones it is very important to make this reminder for you And then how do I identify then among these What is a function of the 2nd degree to which they are always going to have FX Because here we have a function okay FD function da And remembering that depending on the context I change it for the letter is that mine said that time of profit and always a function of the 2nd degree it has to have the highest exponent of x equal to how many people equal to 2 because the function of the 2nd degree like that like when he knows the function of the 1st degree the greatest exponent of X was one Okay so quadratic function the greatest exponent of X has to be two look at this one here look the exponent wants one Okay so if you don't have it there you don't have it problem but the biggest one has to be two let's analyze now this here is a function of the 2nd degree it is characterized as good it has an X squared I have 2x that you Hi guys B but I don't have you don't have that independent term you need to have the term Regardless if it doesn't have it because it's zero who can't be zero look here the only one that can't be zero is air So it means that this here is a function of the 1st degree if a function of the 2nd degree is a function of the 2nd degree degree in this other case Here we have f of x = - 3x squared + 6x - 3 is a function of the 2nd degree people is because the greatest exponent of X is two so also a function of the second or quadratic each time I speak in a little way, right, I prefer saying function of the 2nd degree so that it sounds faster but cool Zinho to talk about this other case here FX = 0 x squared + 2x plus one is a function of the 2nd degree the greatest exponent of X is two so it is a function of the 2nd degree right And why not because here look who is on the side of the x squared just take a look here people baptize me Who is on the side side x squared is Manuel the athlete on the side x squared in this case the air when there is no one on the side x squared is one so here Ah is one in this case who is on the side of x squared is minus three then here uai or minus three and in this case who is on the side x squared and 10 so it's language is zero and what I said The a has to be different from zero as I have this zero here in the place of ar and only that no it's a function of the 2nd degree Why isn't it because that whole part would like it isn't And then there's 2x plus 1 left And then 2x plus one means that the greatest exponent of X will be one there it's first degree so be careful with that if here it is a function of the 2nd degree it is the largest exponent of X here there is no one means it is a So it is not of the 2nd degree it is of the first degree in this x Cubed plus 2 x squared minus 3X plus five this function here too it is not of the second degree because the greatest exponent of our X is 3 and in that case of the last one we also do not have an equation an equation of a function of the 2nd degree because the greatest exponent of XF four then also marks an X for it that is not so in this case I brought only these two they are considered a quadratic function mark this well here Stress this well in your head that now when I say quadratic function You always have this structure in mind here I told you to keep the structure in your mind of a function of the 2nd degree because look here look Indicate the values ​​of the coefficients the scene the quadratic functions that the function of the 2nd degree there I will analyze first then don't waste time let's analyze if it is a function of the 2nd degree is the greatest exponent of X it's two the greatest exponent of X is two so another thing I need to be aware of the coefficient a cannot be 0 coefficient here is two it's ok so it's from the 2nd degree A so tell me who the coefficient a is remembering that that guy who is on the x squared side So who is on the x squared side is the minus two coefficient B is afraid straightened out right Who was the coefficient B is who was on the X side and here on the X side we don't have anyone no now it's one and the coefficient to be is what's left alone because I know if Prontinho was just to indicate right to indicate it could even be done by making an arrow in what went there do ABC to write right in this case here it's an equation I like to talking about being a function of the 2nd degree is a function of the 2nd degree because the greatest exponent is two and here the body feels a different from zero So in this case we have that the coefficient a is the square root of two the coefficient B that that that is on the side of the X here there is no one so it is one but you observed that the minus sign then it is minus one and the coefficient is that it does not have a 0 and in this case here it is a quadratic function it is of the 2nd degree a it is not right because the greatest exponent of X here is one in all of them so what I write when it is not of the 2nd degree is the second degree because it is of the second degree because I need to do the multiplication very well guys I need to do the multiplication between them here for me to determine it's a degree not the way it is there I can't jump to that conclusion saying it's not so let's do our aka shower head I'm going to do XX then X7 So let's do XX is going to be x squared x 7 is going to be 7x now I do here look - 2x x which is minus 2X and minus 2 x 7 which will be minus 14 all that I had here is the result of this multiplication of the product of these terms here there I copy this other one that stayed put that at least 2X and all of that or equal to my function f of x now what can I do here now I can join the terms that are similar in similar terms you can join seven with two with two so here it would be x squared 7 - 2 It's 55 - 2 It's three So it's going to be plus 3x minus 14 so Here we have our function Now you have to tell me it's a quadratic function because the biggest exponent is two and here on the side it's not zero it's perfect tell me now who's the coefficient to coefficient a is one coefficient B is 3 and coefficients e is one minus 14 So like this example here I wanted to show you the following exercise because when we are starting to talk about the quadratic function it starts right here it goes well step by step so if you find an exercise that is already like this you hit your eye cloud the high crazy don't jump to conclusions don't talk which is not of the 2nd degree first we need to develop here the products of the terms here so you have to analyze it well ok to then draw this conclusion and now let's calculate the numerical value of a quadratic function how are we going to do it come on oh give it a take a look at the question I brought you now a contextualized question Do you remember at the beginning of the class that I said that a quadratic function is related to the economy so here is a question to symbolize what I said and here we are going to calculate the numerical value of a quadratic function so it's a contextualized example in which we're going to calculate the numerical value then we're going to see the question in a garment with capacity to produce 7,000 units capacity to produce seven units per month a and the cost of each t-shirt varies according to the quantity produced and it is expressed in thousands of reais, right by the function of X But why is it now without it is not effective too Do you remember that I said that we could change that F by the corresponding letter depending on the context so here I put CD cost the cost the cost depends on the number of shirts produced so there we have variable variables which are the dependent and the independent variable Remembering that here the cost depends on the number of shirts So I have here the formation law of our quadratic function where X is the number of thousands Chile the number of thousands of T-shirts produced what is the cost to produce two thousand T-shirts so let's give one it 's my formation law here it's from X but now I'm not going to write X anymore because I have a value to assign to x What is this value, how many T-shirts?

X1 means the number of thousands of T-shirts produced. How many T-shirts ? t-shirts I'm going to write that x = 2 because q = 2 because two are 2000 2000 units which is two thousands o that's why this information here in statement X is the number of thousands of t-shirts from well one thousand t-shirts two thousands 2000 so I'll change it for two thousands here it's calm so you need to focus on the statement You saw that important information and imagine if I don't remember this information here and come here I put two thousand there I won't be able to arrive at the correct answer so continuing now copy it will be 0.

5 instead of writing the x squared I already change it for the corresponding value that I have here so it will be two instead of the X Remembering that between a number and the letter is times squared minus 4 times the value of X again which would be two plus nine now I Here I solve an expression a normal numeric expression the way you're used to starting with the power 0. 5 x 4 - here 4 x 2 is 8 plus 9 0. 5 x 4 = when it's equal to two, right, what's up and now - 8 plus 9 and now that you put all this together here I have two and I owe eight I know if I owe six and I have 9 I keep three So it means that the cost of producing two thousand would be two thousand t-shirts = 33 reais what is the unit of measurement he is giving for the cost you observed the cost it is expressed in thousands of reais so it means that three here three here are r$ 3000 there if you want to at the end leave represented the lady that the cost for 2000 t-shirts because then it's better for you to visualize it = 3 thousand reais well so Here we have the final answer Remembering that I calculated the numerical value of a function I changed the value of the independent variable in this case for what it gave me in the advertised And there are also cases in which I can change the value of the dependent variable, okay, to find the value of X, I change the function here .

people are symbolic values ​​they are not real values ​​I didn't go there to the t-shirt factory in the confectionery to ask what the values ​​are Remembering that here we have fictitious values ​​ok guys just for us to make the application agreed and now I'll leave you a task so that's it question of making the t-shirts if the company then the making it works at its maximum capacity mem What is how many even seven thousand units per month what will be the course So to produce this maximum amount I want you to leave the answer to this little task in the comments that was just to see if you managed to understand this class and if you will participate in the resolution So but now take the opportunity to know Subscribe to the chalk channel and leave your like and I'll see you in the next class bye bye.