 So what we have is x squared minus four is equal to squared of x plus two and all this is is Asking us when does this function and we already know that's a problem, right? When does this function equal that function and that function that side of the equation? It's just a sideways problem. Okay, we're it's the if you Anyway, we'll talk a lot more about these but it just becomes a Reflection about the y equals x line. Okay, so if we're grabbing both these equations This is what they're gonna look like or graphing both these functions, sorry Let's do this one first when x is Let's pick some numbers that we know this is a square root, so we're gonna try to do perfect squares, right? so when x is two If you put x is equal to two, two plus two is going to be four and the square root of four is two It's plus or minus two, okay, so let's just do plus or minus but we're gonna eliminate the minus part because Definition of a function is it has to only cross it for every x that can only be one y So if we draw full parabola sideways, it doesn't become a function So what we do we eliminate the bottom and again, we're going to talk a lot more about these when we hit polynomials Okay, so this is just sort of a teaser of You know why the difference of square is the equal sign how this all fits together So when x is two y is two plus or minus two so what x is two y is Two and negative, but we're not gonna put that point in there What x is negative two if we put negative two here negative two plus two is going to be zero square root of zero zero So when x is negative two Why is going to be zero and this function goes off like this So if you put let's say you put x is equal to seven here What you're going to do seven plus two is nine and squared of nine plus or minus three, right? So if you go seven seven, it's just going to be three So it's going to be up here. So this graph does curve or this function looks like this This function if we do a table of contests for this guy If you put x is equal to X is equal to zero This is going to be Zero zero squared is zero zero minus four is just gonna be negative four. So what x is zero Why is negative four? What x is two two squared is going to be Four four minus four is zero. So what x is two plus four minus two Why is going to be or this side this function because it's just a function. It's just a Y If you call this f of x, we call this h of x f of x equals this guy h of x equals this guy, right? So if you call if you sub in x is equal to plus or minus two Two squared is four negative negative two all squared is four four minus four is zero. So this just becomes Zero so we have three points here zero one negative four zero and one two three four And we have Two and zero and negative two and so when x is two Why is zero? When x is negative two y So what we have right now is Answering the question when does this function cross this function? Well at this point We don't add negative two and zero they both cross so at that coordinate system Both both functions are crossing each other or hitting each other and at that one to be able to solve it We'd have to square root both sides and we're gonna do a whole bunch of these later on but graphically It's gonna be at x is equal to two points something something something something because it's a little bit past two Okay, so That's what the function means. That's what it means when you say what is something equals something? Okay, when it comes to difference of squares if you have functions that you can factor out Sometimes it becomes simpler to do all you do you grab this whole thing and move it over for this type of question It's easier not to do that There are other types of questions that we talked about where x squared is equal to four You can grab it and bring it over and what what that does we solved it We solved it for x squared is equal to four right so what we did was draw our parabola draw a horizontal line and Found out where the horrible parabola or quadratic function crossed horizontal line, right? The other way to solve that question is move the floor over and Bring it over so it becomes x squared minus four is equal to zero on factor it out And what happens for that if you're graphing that function that? standardizes your Your your solutions that brings them down to the x axis so what it does This was the other one, but it was shifted up right and the horizontal line was up here So we were actually dealing with two different functions right f of x and h of x or f of x and h of x right? If we want to solve it as one Complete function and forget about h of x all we do we bring that four over and solve it And what we end up getting is? Our parabola and whenever we're factoring something when we're solving a question by factor talked about this in series 3a What we're doing is finding the x-intercepts So what that did what that would do by bringing the four over the equal sign for the previous question It would shift our parabola down and all of a sudden our solutions become the x-intercepts, and that's what we're looking for and For a lot of functions for a lot of questions It's easier to solve for the x-intercepts Then not solve for the x-intercept you can punch this into your computer and graph one graph the other and grab the x-intercepts Right, and there's a lot of a lot of schools in my area anyway They use the graphing calculators and all you do you know when they say solve for this if they say you can't use a calculator You got to do it manually. We'll talk about that if they don't say you can't use a calculator All you do is punch that in as your y1 push that in as your y2 Let the let the computer let the program like the calculator Graph it and all you would do is just grab their intercepts where they intercept each other And that would be your solutions for this questions Which is basically asking you at what x-coordinate do both Functions equal each other and what x-coordinate do the both both y is equal to each other, right? So when does y1 equal y2 when does this function equal the other function? We'll talk a lot more about this when we start getting into polynomials