The Square Root Graph Is Simple, If you Can Remember This

what's up guys this is a pretty simple function to be able to graph but a lot of times when I ask students to graph this function they look at me with a Blank Stare it's like they completely forgot how to graph the squared function what it looks like and then also how to create it on their own like I think we get pretty well pretty good with like doing linear equations and then once we get to the square root function people like I just don't remember what this graph looks like and I don't know how to create it using a table of values and part of the reason I think that is the case because students just don't know which values to go ahead and choose so to be able to help you with graphing this to understand the characteristics so we never forget it and we can always graph it on our own I think it's important for us to understand what exactly the square root function is representing so therefore we can pick the right values to go ahead and create a table to therefore then go ahead and graph okay so what I want you to understand is when I take the square root of a number and I get a value a what that represents is a times a right so multiplying by itself is going to give you that value X all right and think about hypothetically like if I had the square root of 9 that's equal to 3 why because 3 times 3 is equal to nine okay so it's very important to how to understand the square root function the next thing that's really important to understand is that my X values when I'm taking the square root or any even root that's always going to be a positive and again you can see like that makes sense because if I'm multiplying something by itself it's always going to be positive right because again it can't be one negative one positive right they either have to be both positive or both negative well a negative times a negative is positive and a positive times a positive is going to also be positive so how can we use this information now to create a table of values well remember when we create table of values with linear equations usually we picked like you know zero negative one negative two and you know zero one and two right we did a positive as well as negative well now we can just focus on the positive results at least for this initial equation we'll get to like the more difficult examples later but for this example we know like all right it has to be a positive I have to choose positive values to plug into the square root function let's go and start with a 0 and a one because that seems like the most easiest to go ahead and start with okay so remember when we have a table of values and I pick values for you know x what I'm going to do is those are going to be values that we're going to plug into our function so here I have X is equal to 0. I'm going to plug 0 in for X so again if you think about this we have you know square root of zero well that's just going to be equal to a 0 right ah so therefore we can say Y is now equal to equal to zero so that's actually something that is actually going to be equal to greater than or actually equal to zero so hopefully you caught me or keep me honest on there if you already posted on the comments I made a mistake then here you go I fixed it always appreciate you keeping me honest in here but yeah X can actually equal to zero as well because you could have a times a is actually or you could have a also being a zero so zero times zero is equal to zero now what I can do is let's go ahead and plot that point on a coordinate grid foreign point zero zero and it's like all right that's not very exciting so let's go to the next Point how about one let's plug one into there the square root of one what what number multiplied by itself gives you one well that's just going to equal one right so square root of one is just equal to one so therefore when I go ahead and plot this here I get a point here now this looks very similar to the identity function right or a linear equation and that's where a lot of students will get mixed up because they're like I don't know what this graph looks like does it go up does it go down like I know it doesn't go to the left right why am I doing that why is that a y I'm crazy um this is the X right I know I can't go to the left I know X cannot be negative right it has to be positive but where does this graph go so here's a mistake that a lot of students will do they'll go ahead and start with the square root of 2. and those like oh square root of two like that makes sense right well like why don't I go ahead and do that problem next well the problem is if I don't know what the square root of 2 is right I can't simplify the square root of two two is not a square number I can't take the square root of 2 and and get an integer right it's going to be an irrational number so therefore I'm going to need a calculator and a lot of times my teacher or myself would say ah no calculator so then I are you going to graph the square root of 2. like you could approximate it but if you have chicken scratch handwriting and cannot really graph very well like your approximation is not going to look very good on a graph like I want to deal with integers so what I want to look for is a square number so what's the next Square number that's going to come up 0 1 2 3 4 right and Y is 4 square number because square root of 4 is 2 right because 2 times 2 is equal to 4 right it follows this definition square root of 4 is equal to 2 because 2 times 2 is equal to 4. so I'm not going to use two don't do that you want to pick your square numbers and that's what's important here that I want you to understand about this equation because even if we have Transformations like plus and minus and multiplying what you want to do is you want to pick values for your table that's going to make your radicand what's under the square root always be an even number so sometimes that takes a little bit of what we call mental gymnastics to do that it's not sometimes as easy as this problem that I'm describing but what you want to do is make sure when you're plugging in values for your table of values that whatever's on your square root you can take the square root of it so try to make sure that they're going to be square numbers I'm not going to put this x that's kind of confusing I'm just going to put a line through it all right so what I'm going to do is I'm going to say what about 4 okay so I have one two three four and we know that the square root of 4 that's just going to equal A2 so 1 2. and voila okay now again you could definitely go to the next one which would be the next squared number which is 9 is going to be 3. so if I was plotting this and you know just to kind of give you a heads up if you did have some transformation I would try to get under my radical you know any one of these three points and technically at least once you have two points as long as you understand what the shape is of this curve then you can go and correct it I think it's always important to have this end point here because that's going to be kind of like the start or the end however you think about it and then at least you're going to want to have one other point because you want to know is it going up sometimes we'll have Transformations that are going down or if we're going to the left like there can be a lot of things going on but as long as you have two points you can recognize that oh what this graph does is it kind of goes faster increasing and then it tapers down and stuff like that so that exactly what this graph looks like now that you kind of see it and recognize it when we apply Transformations hopefully you can see that oh yeah I know some important points I know how to quickly find them if I need to and then I can apply my Transformations as needed so in the next video that's exactly what I want to deal with is how to identify the transformations to transform this graph as well as how to find the domain and the range