# Online graphing calculator wrong? **URL:** \ **Category:** Factual Questions\ **Created:** [January 16, 2025, 7:39pm UTC](https://boards.straightdope.com/t/online-graphing-calculator-wrong/1013053 "2025-01-16T19:39:48Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [January 16, 2025, 7:39pm UTC](https://boards.straightdope.com/t/online-graphing-calculator-wrong/1013053/1 "2025-01-16T19:39:48Z")
This YouTube [https://www.youtube.com/watch?v=\_Y778c5g3zU](https://www.youtube.com/watch?v=_Y778c5g3zU) video goes through the steps of finding all the solutions for a sixth-order equation, name (x-2)6 = 729. As expected there are two real solutions and four complex solutions. However, when I went to [Desmos | Graphing Calculator](https://www.desmos.com/calculator) and entered that, it gives two vertical lines at the two real solutions and thus an infinite number of complex solutions. Is Desmos faulty or at least limited in the degree of equations it can plot, or am I doing something wrong? ---
**Author:** ![Pleonast](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pleonast/32/1183_2.png) [@Pleonast](https://boards.straightdope.com/u/Pleonast)\ **Post date:** [January 16, 2025, 7:54pm UTC](https://boards.straightdope.com/t/online-graphing-calculator-wrong/1013053/2 "2025-01-16T19:54:52Z")
It’s not clear to me what that calculator is plotting. ---
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [January 16, 2025, 7:59pm UTC](https://boards.straightdope.com/t/online-graphing-calculator-wrong/1013053/3 "2025-01-16T19:59:02Z")
The vertical lines are at x= -1 and x=5, the two obvious real roots, so it’s displaying something relevant to the equation. But not the discrete solutions the video showed. ---
**Author:** ![gnoitall](https://avatars.discourse-cdn.com/v4/letter/g/bb73d2/32.png) [@gnoitall](https://boards.straightdope.com/u/gnoitall)\ **Post date:** [January 16, 2025, 8:47pm UTC](https://boards.straightdope.com/t/online-graphing-calculator-wrong/1013053/4 "2025-01-16T20:47:15Z")
That doesn’t look like a complex plane graph, so I imagine the grapher discarded the complex roots. ---
**Author:** ![Great\_Antibob](https://avatars.discourse-cdn.com/v4/letter/g/e47c2d/32.png) [@Great\_Antibob](https://boards.straightdope.com/u/Great_Antibob)\ **Post date:** [January 16, 2025, 9:09pm UTC](https://boards.straightdope.com/t/online-graphing-calculator-wrong/1013053/5 "2025-01-16T21:09:14Z")
As above, graphing calculators show the real plane, not the complex plane. And in the real plane, the only valid solutions are x=-1 and x=5, which graph as vertical lines. ---
**Author:** ![Max\_S](https://avatars.discourse-cdn.com/v4/letter/m/46a35a/32.png) [@Max\_S](https://boards.straightdope.com/u/Max_S)\ **Post date:** [January 16, 2025, 9:25pm UTC](https://boards.straightdope.com/t/online-graphing-calculator-wrong/1013053/6 "2025-01-16T21:25:36Z")
They aren’t actually vertical lines. If you adjust the scale (using the wrench button in the top right corner) to -750\ **Author:** ![Great\_Antibob](https://avatars.discourse-cdn.com/v4/letter/g/e47c2d/32.png) [@Great\_Antibob](https://boards.straightdope.com/u/Great_Antibob)\ **Post date:** [January 16, 2025, 9:27pm UTC](https://boards.straightdope.com/t/online-graphing-calculator-wrong/1013053/7 "2025-01-16T21:27:16Z") Incidentally, just caught the YouTube video. It’s nice, but way too complicated a method for my tastes. I prefer a more geometric approach as per Euler. If we assume a function mapping complex numbers, then there are 6 solutions, as noted. They lie at the vertices a regular hexagon of outer radius 3 on the complex plane centered at x=2. So, there are the solutions (-1,0) and (5,0) plus 4 others are the other points of the hexagon which would be +/- 60 degrees off the real axis using (2,0) as the vertex. And so we basically just need to know/remember a bit of trig and that cos(60 deg) = cos(pi/3) = 1/2 and sin(pi/3) = sqrt(3)/2 to find the rest (to be fair, not everybody may know or remember these). With that knowledge, two more solutions would be given by 2+3_cos(pi/3) +/- i_3_sin(pi/3), which is [7 +/- i_3\*sqrt(3)]/2. And the two remaining solutions at 2+3_cos(2_pi/3) +/- i_3_sin(2_pi/3), which is [1 +/- i_3\*sqrt(3)]/2 > [@Max\_S](#): > > They aren’t actually vertical lines. If they’re not, then there really is an issue with the software. They should be vertical lines. ---
**Author:** ![Max\_S](https://avatars.discourse-cdn.com/v4/letter/m/46a35a/32.png) [@Max\_S](https://boards.straightdope.com/u/Max_S)\ **Post date:** [January 16, 2025, 9:38pm UTC](https://boards.straightdope.com/t/online-graphing-calculator-wrong/1013053/8 "2025-01-16T21:38:13Z")
My mistake, I had typed it as a function of x. f(x)=(x-2)^6 - 729 is “U” shaped. ~Max ---
**Author:** ![Great\_Antibob](https://avatars.discourse-cdn.com/v4/letter/g/e47c2d/32.png) [@Great\_Antibob](https://boards.straightdope.com/u/Great_Antibob)\ **Post date:** [January 16, 2025, 9:39pm UTC](https://boards.straightdope.com/t/online-graphing-calculator-wrong/1013053/9 "2025-01-16T21:39:35Z")
Yeah, that makes sense then. Solutions given where it crosses the x-axis, i.e. where f(x) = 0 ---
**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\ **Post date:** [January 16, 2025, 9:43pm UTC](https://boards.straightdope.com/t/online-graphing-calculator-wrong/1013053/10 "2025-01-16T21:43:06Z")
I’m not sure I understand the question. The solutions are obviously x-2 = 3\*u where is u is any of the six sixth roots of 1, that is \pm1, \frac{\pm1\pm\sqrt{3}}2 ---
**Author:** ![Great\_Antibob](https://avatars.discourse-cdn.com/v4/letter/g/e47c2d/32.png) [@Great\_Antibob](https://boards.straightdope.com/u/Great_Antibob)\ **Post date:** [January 16, 2025, 9:47pm UTC](https://boards.straightdope.com/t/online-graphing-calculator-wrong/1013053/11 "2025-01-16T21:47:06Z")
The OP did not realize graphic calculators do not plot complex valued solutions and thought there may have been a bug. ---
**Author:** ![Topologist](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/topologist/32/3208_2.png) [@Topologist](https://boards.straightdope.com/u/Topologist)\ **Post date:** [January 16, 2025, 9:48pm UTC](https://boards.straightdope.com/t/online-graphing-calculator-wrong/1013053/12 "2025-01-16T21:48:08Z")
> [@Max\_S](#): > > My mistake, I had typed it as a function of x. f(x)=(x-2)^6 - 729 is “U” shaped. Even if you type it in as the equation (x-2)^6 = 729, Desmos interprets that as your wanting to graph y = (x-2)^6 - 729. Not unreasonable, as the solutions of the equation are where the graph of the function crosses the x-axis. ---
**Author:** ![Zoobi](https://avatars.discourse-cdn.com/v4/letter/z/13edae/32.png) [@Zoobi](https://boards.straightdope.com/u/Zoobi)\ **Post date:** [January 16, 2025, 9:49pm UTC](https://boards.straightdope.com/t/online-graphing-calculator-wrong/1013053/13 "2025-01-16T21:49:09Z")
Here’s a plot of the solutions: [![](https://i.ibb.co/k08Qsgt/0bef1d9458db.png) ](https://i.ibb.co/k08Qsgt/0bef1d9458db.png) ---
**Author:** ![gnoitall](https://avatars.discourse-cdn.com/v4/letter/g/bb73d2/32.png) [@gnoitall](https://boards.straightdope.com/u/gnoitall)\ **Post date:** [January 16, 2025, 9:51pm UTC](https://boards.straightdope.com/t/online-graphing-calculator-wrong/1013053/14 "2025-01-16T21:51:03Z")
Exactly as @Great_Antibob described. > [@Great\_Antibob](#): > > there are the solutions (-1,0) and (5,0) plus 4 others are the other points of the hexagon which would be +/- 60 degrees off the real axis using (2,0) as the vertex. ---
**Author:** ![Max\_S](https://avatars.discourse-cdn.com/v4/letter/m/46a35a/32.png) [@Max\_S](https://boards.straightdope.com/u/Max_S)\ **Post date:** [January 16, 2025, 10:04pm UTC](https://boards.straightdope.com/t/online-graphing-calculator-wrong/1013053/15 "2025-01-16T22:04:03Z")
And here in Desmos, > **[Desmos | Graphing Calculator](https://www.desmos.com/calculator/ff0kixv5j7)** > > Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. ~Max ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [January 16, 2025, 10:15pm UTC](https://boards.straightdope.com/t/online-graphing-calculator-wrong/1013053/16 "2025-01-16T22:15:14Z")
> [@Topologist](#): > > Even if you type it in as the equation (x-2)^6 = 729, Desmos interprets that as your wanting to graph y = (x-2)^6 - 729. Not unreasonable, as the solutions of the equation are where the graph of the function crosses the x-axis. No, that’s not what Desmos is doing. When you type an equation with a single variable, Desmos assumes that you’re defining that variable. So it interprets “(x-2)^6 = 729” as “x = -1 and x = -5”. And “x=-1” is a straight vertical line, and so is “x=5”. EDIT: Here’s a demonstration with a simpler equation > **[Desmos | Graphing Calculator](https://www.desmos.com/calculator/pvph9atdi3)** > > Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. ---
**Author:** ![Topologist](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/topologist/32/3208_2.png) [@Topologist](https://boards.straightdope.com/u/Topologist)\ **Post date:** [January 16, 2025, 10:25pm UTC](https://boards.straightdope.com/t/online-graphing-calculator-wrong/1013053/17 "2025-01-16T22:25:06Z")
> [@Chronos](#): > > No, that’s not what Desmos is doing. You’re right, I’m wrong. I thought it was giving me the same graph as the function, but now I can’t reproduce that. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [January 17, 2025, 1:20am UTC](https://boards.straightdope.com/t/online-graphing-calculator-wrong/1013053/18 "2025-01-17T01:20:01Z")
> [@Chronos](#): > > EDIT: Here’s a demonstration with a simpler equation Even simpler would be an equation like “x = 2.” The graph of an equation like that in the xy-plane is a vertical line, because it’s made up of all the points (x, y) which satisfy that equation. So it only makes sense that if you type in the equation (x-2)^6 = 729 you would get \{(x, y) \in \mathbb{R}^2 | (x-2)^6 = 729\}, which would consist of those two vertical lines. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [January 17, 2025, 3:43am UTC](https://boards.straightdope.com/t/online-graphing-calculator-wrong/1013053/19 "2025-01-17T03:43:15Z")
> [@Thudlow\_Boink](#): > > Even simpler would be an equation like “x = 2.” Yes, but I was demonstrating that Desmos does implicit definitions, too. I wasn’t surprised the first time I saw it draw a vertical line for “x = 2”, but I was surprised the first time I saw it from a quadratic. The ability to deal with implicit relations in general is one of Desmos’ greatest strengths, compared to typical graphing calculators. You can put in any equation you want, with any complicated mishmash of x and y that couldn’t possibly be solved for either variable, and it’ll still show you a graph of the set of all points that satisfy the equation. ---
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [January 17, 2025, 3:47am UTC](https://boards.straightdope.com/t/online-graphing-calculator-wrong/1013053/20 "2025-01-17T03:47:09Z")
So is there a way in Desmos of restating the equation that gives the six points of @Zoobi 's plot? [Next page](https://boards.straightdope.com/t/online-graphing-calculator-wrong/1013053.md?page=2)