Shading in Desmos

okay so shading in Desmos is little bit of hard thing to figure out even after you know how to do it so bear with me as go through this video because who knows what kind of errors I'm going to make and don't want to have to start over 30 times so you can see on the graph I've already made little heart very simple hopefully your project is way more complex than this you can see in this folder that call have called heart have all my lines and then this folder called shading is where I'm going to put all of my lines that show how want to shade in the heart so first I'll talk to you about the shading lines so you'll see when open both folders this that the lines are almost well right now they are identical this blue line up here equal 34 X+ 3 down here blue 34 plus 3 they exact same thing okay the way did that is just cloned each line so if you look down here at my shading only have five lines haven't done the last green one so the way you do that is you this little edit button and then you just pick the line you want to clone so want to clone this green one I'm going to click duplicate it's going to pop up right underneath it so I'm going to then move it down into this other folder underneath the rest of them okay the other thing want to do is I'm going to make my shading lines all be dotted honestly that is more for me to recognize where they are than anything else you don't have to do that unless your teacher wants you to but it just helps me to kind of see what I'm working with so now when you look at my picture each line has both I'll this one has solid version underneath and then the dotted version on top so know that I've made every line duplicate and you don't have to do this in the future you'll realize you don't have to do this for every single line but it's just good way to show you what we're working with here so I'm going to go ahead and close my normal lines up there with my dotted lines the only thing have to do to make them shaded is to make them into inequality so let's just start with this blue line the very first line have here I'm going to close it just you can see it so one up there if want to shade underneath it so can color in my heart all have to do is think about well do want to be less than in shade below the line or greater than in shade Above So less than means I'm going to remove my equal sign and instead use hand symbol you'll see have shaded underneath it but right off the bat you see some issues it goes too far right it's going to go on forever and ever and ever so we want to fix that and it's only limited from here to here with my domain okay don't want to talk about domain here in second let's first talk about how do stop it from going below this orange line right well we have said that needs to be less than -34 + 3 we haven't said anything about what needs to be greater than well we know that needs to be greater than this orange line so down here can see that this is my equation for my orange line instead of me doing just is greater than down here and having this issue I'm actually going to combine both my blue and my orange into one inequality compound inequality so I'm going to take that back okay I've got the equals I'm going to use the same little piece - 2 and move it up here to my blue line to make it compound so let me go and retype - 2 and put greater than now you can see that this shading has been limited on the top by the -34 plus 3 is less than that and then on the bottom by my orange line over here xus 2 really don't really need this orange line as far as greater than it's concerned until get to this bit right here now the domain you going be thinking okay well it's cut off on the left and right if move it to the right okay so let's say want to keep this shading going all the way to positive two you'll see that it's just going to go past the point want it to and then I'd have to cut it off here cut it off here really what's best is to actually do it in segments and leave the domains alone okay and again you'll see as you go along and you play with this more and more that you can find more shortcuts more methods more ways to do this and what I'm showing you I'm trying to just give you the basics that will work every time even if it takes longer and if you have the time in your project to keep going and learn some new things please go for it show us what you learn explore to your heart's content okay so I've got this piece I'm going to go then look for the next piece that want to shade underneath which would be this green line right here okay and that is it this one this one X+ 2 think it's this one no it's this One plus 10 because could tell from my intercept okay here's my line again bear with me so want to be less than this line so I'm going to shap changes to less than but again it's going too far so want to stop it with this same orange line from before so the exact same equation used second ago YX - 2 I'm going to combine once again with this green line okay so I'm going to type-x minus 2 and make it the lower bound of this shading so have my upper bound with that green line lower Bound by the Orange Line okay at this point really don't need the orange anymore right if was to actually shade Above This Orange Line I'd have to go through this process all again and it's already shaded so need it so I'm actually going to remove the orange line all together okay while I'm thinking about it can change this coloring just like can with the lines by doing edit changing this let's make it red heart going down here changing this to red and now I'm shading everything in red okay you can go to the end it's probably safer to stick with the MTH first so let's keep going want to shade underneath this red line would always start with the upper bound just to be consistent so want to shade underneath the red here we go want to shade underneath so is less than but need to stop that shading with this green line as my lower bound so here's the equation for the green line plus 2 going stick that behind my and I've stopped it okay want to shade underneath the purple so again underneath requires it to be less than but want to stop it by that Green Boundary again so + 2 is less than and I've stopped it don't need the green anymore change this red oops do edit first and now have cute red heart awesome blossome if you again want to change all the colors from before so you don't see this green peeking through you can go for it but that those are the basics of shading again it's kind of one of those things that you have kind of use trial and error to figure out hopefully this gives you enough to get started if you have questions need some help figuring out problem feel free to go ask your teacher