Desmos User Guide
Contents
1. ange color expressions here convert to table co Change color 73 2 Delete Chocsea new coir OD 2 E xX Click here to for the expression 7 E pete your Convert to table Duplicate Generate a table from Add a copy of the the expression expression below the current one desmos Variables and Sliders You can graph a single line by entering an expression like y 2x 3 To make the graph more dynamic you can use parameters instead of constants for example y mx b Add sliders for the undefined parameters by clicking the prompt or define the parameters yourself by entering m 2 and b 3 When you give constant values to parameters like m and b the calculator will automatically allow you to adjust their values with sliders Adjusting m with the slider changes the slope of the line and adjusting b with the slider changes the intercept Any time you have free variables in an y yx 5 expression the calculator will offer to let you define them with sliders m b 1 The value of c defines two parallel lines that These two lines stay perpendicular to each move up and down together other for any value of m PS To adjust the limits and interval of your slider click E yomtb either of the values at the ends of the slider bar 3 Input your desired values and click the expression O m or the graph to complete the adjustment 10 sms 10 step desmos 2 To create a movable point enter a point with a2. will make the graph and axes lines thicker and the number labels larger This is great for students sitting in the back of the classroom who are x axis looking at Desmos on the projector Boi vs m lt x lt 10 Sep Show Numbers Graph Paper In the graph paper section you can change the grid and axes Click the green circular icons to choose between Cartesian and Polar grids and show or hide axes and labels Step 2 Click the gray arrow next to an axis to adjust the window size add a step try pi or add arrows bes cee Angles Choose between radians and degrees here Zoom You may zoom in and out of the calculator by using the zoom buttons in the zoom menu If your axes are no longer square click the square option To return to the default view click the default option Other ways to zoom If you are using a touch enabled device you may also use the pinch and zoom technique within the graphing space using a computer with a mouse you can use the scroll wheel for zooming Click and drag within the graphing window to pan your graph within the graphing space Language To change the language of the calculator interface click the icon and select your language from the list If you don t see your language and would like to help with translation email us at translations desmos com desmos Tables Dive deeper into data with tables You can create a new table or convert an e
3. an also create your own functions which can be defined with any letter except for the special ones like xy t and e Your custom functions can then be used like any other function on this list For example if you type f x x42 you can then graph y f x 1 which is the same parabola but shifted over to the left 11 Keyboard Shortcuts Open Graph ctrl o Symbols Save ctrl s J Type sum Save As or Rename ctrl shift s Tt Type pi Undo ctrl z Type theta Redo ctrl y J Type sqrt New expression Press enter N Type prod Move up down Press the f and arrow keys Move left right Press the 4 and arrow keys Add a new text box Press the quotation keys Delete an expression Press delete All done You re ready to take off and explore Desmos If you have questions that we didn t answer in here send us an email at calculator desmos com desmos 2
4. desmos Learn more about graphing functions plotting tables of data evaluating equations exploring transformations and more If you have questions that aren t answered in here send us an email at calculator desmos com Getting Started with Desmos 1 Variables and Sliders 2 Graphable Expressions 4 Settings Zoom andLanguage 6 Tables te Lists and Statistics 8 Regressions i 9 Notes Folders and Images mm 10 Supported Functions 1 Keyboard Shortcuts 12 f facobookcom desmosine W edesmos catculator desmos com Getting Started with Desmos Making a graph Welcome to Desmos To create a new graph just type your expression in the expression list bar As you are typing your expression the calculator will immediately draw your graph on the graph paper Open Graph Save As or Rename Save Revisit your saved Click here to save a copy of Click here to save graphs and example your graph or rename it You your graph or graphs here can also press ctrl shift s press ctri s Untitled Graph fl Add Item a Addanew SS Hide list expression table text F mw Push your expressions list to the side to give box folder or image _ 22 full attention to Hide your graph Click here z to hide individual expressions Long hold to change the sinx color or style Undo and Redo Edit List Delete all You can also press ctrl 2 pales aioe Delete all of your to undo and ctrl y to redo G
5. from the expression drop down or by pressing the quote key in an empty expression box Folder Folders allow grouping expressions collapsing groups and showing hiding a whole group at once You can drag equations into the folder a gray ya2et3 line will show up to the left of the equation to let you know it s in the folder You can click the arrow next to the folder name to expand collapse the folder contents and clicking the folder icon will show hide the contents e Amazing photo by Dan Meyer 10 Supported Functions Exponents amp Logs exp In x log log P ra Precalc amp Calculus d dx by n Misc Icm a b gcd a b mod a b ceil x floor x round x abs x sign x desmos Stats amp Probability total x sum ofall elements in a list length x number of elements in a list mean median x min x max x quantile x p mad mean absolute deviation stdevix sample standard deviation stdevp x population standard deviation var x variance cov k X covarianca corr xa Pearson correlation coeficient of two lists nCr n r Number of combinations nPr n r Number of permutations n Factorial Trig Functions sin x arcsin x _ sinh x cos x arccos x cosh x tan x arctan x tanh x sec x arcsec x sech x esc x arccse x esch x cot x arccot x coth x Define your own function You c
6. graph to share a custom message in any of our partner forums desmos Graphable Expressions Type of Graph Example Notes Regular function y 2x 1 xin terms of y x V F boat xs2y Strict inequalities are Inequalities plotted with dashed 2x 4 lt y lt 4 lines Expressions with r Polar r sin 50 and theta 8 will be interpreted as polar Use the condition X value default format for Piecewise esaa E 7 er Add the restriction at D Domain and range Y t 2 lt x lt 2 the end of the equation J restrictions x sin y ri lt y lt n Try the restrictions tour F in the help menu CJ desmos 4 Type of Graph Point Point List Movable Point Parametric Implicit List Expressions Regression desmos Example 1 0 1 1 2 2 3 3 a b sin 2t cos 3t x y2 1 y x 1 3 5 yy mx b Notes Use parentheses to plot points You can plot several points by separating them with commas Use a parameter for at least one coordinate Parametric equations have the same form as points Any point with functions of t for coordinates will be plotted as a parametric equation Solutions of equations involving x and y can be plotted without solving for x or y Learn more about lists on page 8 Leam more about regressions on page 9 Settings Zoom and Language Settings Projector Mode Projector Mode Graph Paper Using projector mode
7. u connect two lists of data with a we adjust every free parameter to make the lists as close to each other as possible Since table columns are each lists the easiest way to make a regression is to create a new table of data and then write an equation like yz mxy b Here we ll adjust m amp b to find the best linear model If you instead type y ax bx c we ll find the best quadratic fit If xand y are table columns then y mx bisa a a regression that finds the least z squares values of m and b miaa sma j a and plots the best fit line yrs b an ss aa ast u u You can click ss to plot residuals or use residuals in other expressions For example mean e2 is the mean of the squares of the residuals Try the regressions tour in the help menu for a guided introduction to creating regressions in the O eT calculator Sides Tablas Restcons Regressions Tours desmos 9 Notes Folders and Images expression note table BE folder image Image Add an image from the drop down or drag your image into the expression list Basketball jpg center 17 107 size 525 x 295 You can edit image position and size by manually setting it in the expression list or dragging the blue points on the graph paper desmos In addition to expressions and tables you can add helpful non math items to your expression list Note Add a note
8. variable for at least one coordinate Click and drag the Pent joint around the graph to change 4 fhe value of the pararnster T ab make graphs more interactive use parameters from your movable point in your expressions For example you can graph the line y b m x a and plot the movable point a b to see the line move when you drag the point don t forget to add sliders Saving a graph You will need to be signed in to save and open your graphs P Save a graph by pressing the jj button located to the right of the title bar or pressing ctrl s on your keyboard Access your saved graphs by clicking the my graphs icon Sharing a graph Clicking in the top toolbar will allow you to share your graphs Permalink Underneath the social sharing options you will see a permalink for your graph You can copy this link and share it with anyone When they open it they will see your graph and all of the Share your graph with the world Share this link equations https Jwivw desmos com calculator SIvSiseOn Image Grab a screenshot of your graph by clicking the gua gaies ies Image button An image of your graph will open in a new window which you can print or right J q click to save as an image Email Embed Email your graph by Copy the HTML embed code clicking here You to post your graph in a website can send to multiple or wiki You can also use the recipients and even add BBCode for your
9. xisting expression into a table You can even copy paste two column data from a spreadsheet into an empty expression box to quickly create a new table t Te Add Column _ Oa LO e anon i column by hitting f x expression the right arrow 2 4 key or clicking in S698 text 3 A the top cell of the column a p Add Table Add Row Click the Add Item Make a new row by hitting the down button to create a arrow key or clicking in the cell new table kad lt es Options Menu x Click the icon to i change color connect 1 ba or hide the points or 1 aye insert a new column 2 arag 3 4 or cos x Ano x In edit mode click the convert to table icon to create a table from your expression desmos 7 Lists and Statistics You can make lists in Desmos using square brackets like this 1 1 2 3 5 8 You can create lists with evenly spaced elements 1 10 is a list of the integers between 1 and 10 1 3 11 is a list of the odd integers between 1 and 11 F 5 You can use lists anywhere in expressions that a 1 2 3 you would use a number y v Q y a sin x J ETA Statistics functions like mean median min max and Gi stdev take a list as an argument and return a number length 1 1 1 1 E3 r Table columns are available as lists in the rest of the system min x a total y desmos Regressions is our magic regression symbol Basically if yo
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