incorrect rounding on a graph page

Peggy Frisbie

unread,

Apr 20, 2021, 3:53:06 PM4/20/21

to tinspire

When using a graph to find the vertex of the parabola y = –8x² + 2x + 2.1, the TI-nspire CX II CAS gives a vertex of (0.125, 2.22), as seen in the image here. The 1/8 for the x-coordinate is exact, and the y-coordinate should be exactly 2.225. The calculator is set to Float 3, and the exam that this is from requires 3 significant figures.

Screen Shot 2021-04-20 at 3.47.50 PM.png

I am at a loss to explain to my students why they (and I) are not getting a correctly rounded answer of 2.23. When more digits are shown (either with the hover-plus method or by changing the settings), we see the correct exact answer. Is this an OS glitch of some sort? Is there something we should be doing differently?

John Hanna

unread,

Apr 20, 2021, 7:41:37 PM4/20/21

to tins...@googlegroups.com

Hover the mouse over the ‘2.22’ and press the [+] key to see more decimal places.

Moral: don’t trust the graph to tell the whole story. There are other, better tools to use.

Be Excellent,

John Hanna

From: tins...@googlegroups.com <tins...@googlegroups.com> On Behalf Of Peggy Frisbie
Sent: Tuesday, April 20, 2021 3:53 PM
To: tinspire <tins...@googlegroups.com>
Subject: [tinspire] incorrect rounding on a graph page

When using a graph to find the vertex of the parabola y = –8x² + 2x + 2.1, the TI-nspire CX II CAS gives a vertex of (0.125, 2.22), as seen in the image here. The 1/8 for the x-coordinate is exact, and the y-coordinate should be exactly 2.225. The calculator is set to Float 3, and the exam that this is from requires 3 significant figures.

I am at a loss to explain to my students why they (and I) are not getting a correctly rounded answer of 2.23. When more digits are shown (either with the hover-plus method or by changing the settings), we see the correct exact answer. Is this an OS glitch of some sort? Is there something we should be doing differently?

--
--
To post to this group, send email to tins...@googlegroups.com
To unsubscribe send email to tinspire+u...@googlegroups.com
For more options, visit this group at
http://groups.google.com.au/group/tinspire?hl=en-GB?hl=en-GB
The tns documents shared by group members are archived at
https://sites.google.com/site/tinspiregroup/classroom-news/welcome-abouttime

---
You received this message because you are subscribed to the Google Groups "tinspire" group.
To unsubscribe from this group and stop receiving emails from it, send an email to tinspire+u...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/tinspire/7ae61fb9-a26a-45f6-b1f1-357a55987cb7n%40googlegroups.com.

image001.png

Peggy Frisbie

unread,

Apr 21, 2021, 5:56:14 AM4/21/21

to tins...@googlegroups.com

I did do the hover thing; that was in the paragraph below the image.

For IB exams, CAS is not allowed, so our CX II CAS calculators are put in press-to-test mode with CAS disabled, along with many other things. What remains unchecked on the PTT screen are inequality graphing, log_b and summation templates, variations on trig functions, and the polynomial root finder and simultaneous equation solver.

Given those restrictions, what better calculator tool do you have in mind? My students could, of course, use an axis formula to find the x-coordinate of the vertex and then substitute. They could use a derivative to locate the maximum x-value and substitute. However, these are really not what is expected for the number of marks available for this question and the amount of work the markscheme requires. The issue is not that the calculator is not precise enough; all of the digits are available. The issue is that the calculator apparently has not rounded those digits correctly.

Peggy

_____________________
Peggy Frisbie
_____________________

You received this message because you are subscribed to a topic in the Google Groups "tinspire" group.
To unsubscribe from this topic, visit https://groups.google.com/d/topic/tinspire/wyK2xvT-qEU/unsubscribe.
To unsubscribe from this group and all its topics, send an email to tinspire+u...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/tinspire/00a701d7363e%24b3b736c0%241b25a440%24%40optonline.net.

Adam Pennell

unread,

Apr 21, 2021, 10:29:29 AM4/21/21

to tins...@googlegroups.com

Hi,

The graph is using an algorithm that gives a very close approximation. Graphs are not exact. If you change the display digits to Fix 12, you can see what is going on (See below). As John said, there are better tools to use for exact answers.

Have a great day!

Adam

On Tue, Apr 20, 2021 at 7:41 PM John Hanna <jeh...@optonline.net> wrote:

To view this discussion on the web visit https://groups.google.com/d/msgid/tinspire/00a701d7363e%24b3b736c0%241b25a440%24%40optonline.net.

Peggy Frisbie

unread,

Apr 21, 2021, 1:39:10 PM4/21/21

to tinspire

Thanks, Adam. I told my students today that the only idea that I had was that the value on that screen was 2.22499..something, but I didn't find the right setting. (I tried just Float.) What I find with Fix 12 in CAS-Off mode is this:

Screen Shot 2021-04-21 at 1.36.01 PM.png

Float 12 gives the same thing. That definitely shows the rounding issue, if not in the second coordinate.

I am still at a loss as to what you guys are referring to as "better tools" if the CAS is turned off and there are restrictions on some things, as listed in my last post. The only things I could think of were not based in using the calculator, but algebra. (I'm not complaining about algebra here, just wondering what you had in mind.)

Landy Godbold

unread,

Apr 21, 2021, 10:04:57 PM4/21/21

to tinspire

I'm no expert, so this may be totally wrong, but isn't the "3" in "Float3" the TOTAL number of digits displayed, not the number right of the decimal point? Shouldn't Float4 do what you want?

> *From:* tins...@googlegroups.com <tins...@googlegroups.com> *On Behalf
> Of *Peggy Frisbie
> *Sent:* Tuesday, April 20, 2021 3:53 PM
> *To:* tinspire <tins...@googlegroups.com>
> *Subject:* [tinspire] incorrect rounding on a graph page
>
>
>
> When using a graph to find the vertex of the parabola *y* = –8*x*² + 2*x* +

> 2.1, the TI-nspire CX II CAS gives a vertex of (0.125, 2.22), as seen in

> the image here. The 1/8 for the *x*-coordinate is exact, and the *y*-coordinate

> should be exactly 2.225. The calculator is set to Float 3, and the exam
> that this is from requires 3 significant figures.
>

> I am at a loss to explain to my students why they (and I) are not getting
> a correctly rounded answer of 2.23. When more digits are shown (either with
> the hover-plus method or by changing the settings), we see the correct
> exact answer. Is this an OS glitch of some sort? Is there something we
> should be doing differently?
>
> --
> --
> To post to this group, send email to tins...@googlegroups.com
> To unsubscribe send email to tinspire+u...@googlegroups.com
> For more options, visit this group at
> http://groups.google.com.au/group/tinspire?hl=en-GB?hl=en-GB
> The tns documents shared by group members are archived at
>
> https://sites.google.com/site/tinspiregroup/classroom-news/welcome-abouttime
>
> ---
> You received this message because you are subscribed to the Google Groups
> "tinspire" group.
> To unsubscribe from this group and stop receiving emails from it, send an
> email to tinspire+u...@googlegroups.com.
> To view this discussion on the web visit
> https://groups.google.com/d/msgid/tinspire/7ae61fb9-a26a-45f6-b1f1-357a55987cb7n%40googlegroups.com

> <https://groups.google.com/d/msgid/tinspire/7ae61fb9-a26a-45f6-b1f1-357a55987cb7n%40googlegroups.com?utm_medium=email&utm_source=footer>
> .

>
> --
> --
> To post to this group, send email to tins...@googlegroups.com
> To unsubscribe send email to tinspire+u...@googlegroups.com
> For more options, visit this group at
> http://groups.google.com.au/group/tinspire?hl=en-GB?hl=en-GB
> The tns documents shared by group members are archived at
>
> https://sites.google.com/site/tinspiregroup/classroom-news/welcome-abouttime
>
> ---
> You received this message because you are subscribed to a topic in the
> Google Groups "tinspire" group.
> To unsubscribe from this topic, visit
> https://groups.google.com/d/topic/tinspire/wyK2xvT-qEU/unsubscribe.
> To unsubscribe from this group and all its topics, send an email to
> tinspire+u...@googlegroups.com.
> To view this discussion on the web visit
> https://groups.google.com/d/msgid/tinspire/00a701d7363e%24b3b736c0%241b25a440%24%40optonline.net

> <https://groups.google.com/d/msgid/tinspire/00a701d7363e%24b3b736c0%241b25a440%24%40optonline.net?utm_medium=email&utm_source=footer>
> .

>

--
--
To post to this group, send email to tins...@googlegroups.com
To unsubscribe send email to tinspire+u...@googlegroups.com
For more options, visit this group at
http://groups.google.com.au/group/tinspire?hl=en-GB?hl=en-GB
The tns documents shared by group members are archived at
https://sites.google.com/site/tinspiregroup/classroom-news/welcome-abouttime

---
You received this message because you are subscribed to the Google Groups "tinspire" group.
To unsubscribe from this group and stop receiving emails from it, send an email to tinspire+u...@googlegroups.com.

To view this discussion on the web visit https://groups.google.com/d/msgid/tinspire/CABfkkOi1trCCx_csLJsxEmYtJhJcmd04cL4FW4XvTU4DyUc7vw%40mail.gmail.com.

Karen Campe

unread,

Apr 21, 2021, 11:57:33 PM4/21/21

to tinspire

If you want 3 decimal digits, you need "Fix 3" because Float refers to number of digits total (I believe).

AND, although the initial display of the vertex shows 2.22, once you hover and add digits, then hover and subtract them, it reverts to 2.23.

Karen

Peggy Frisbie

unread,

Apr 22, 2021, 5:17:08 AM4/22/21

to tinspire

We need three significant figures, not three decimal places; that is Float 3 rather than Fix 3.

Karen, nice catch on the adding and then subtracting digits. I wonder why it works that way.

epi van winsen

unread,

Apr 22, 2021, 9:39:58 AM4/22/21

to TI Googlegroup

See the difference between the function with 2.1 and the function with 21/10.

The difference between these “lookalikes” generates the “problem”

Best regards

Epi van Winsen

Op 21 apr. 2021, om 01:41 heeft John Hanna <jeh...@optonline.net> het volgende geschreven:

Hover the mouse over the ‘2.22’ and press the [+] key to see more decimal places.
Moral: don’t trust the graph to tell the whole story. There are other, better tools to use.

Be Excellent,
John Hanna

From: tins...@googlegroups.com <tins...@googlegroups.com> On Behalf Of Peggy Frisbie
Sent: Tuesday, April 20, 2021 3:53 PM
To: tinspire <tins...@googlegroups.com>
Subject: [tinspire] incorrect rounding on a graph page

When using a graph to find the vertex of the parabola y = –8x² + 2x + 2.1, the TI-nspire CX II CAS gives a vertex of (0.125, 2.22), as seen in the image here. The 1/8 for the x-coordinate is exact, and the y-coordinate should be exactly 2.225. The calculator is set to Float 3, and the exam that this is from requires 3 significant figures.

<image001.png>

I am at a loss to explain to my students why they (and I) are not getting a correctly rounded answer of 2.23. When more digits are shown (either with the hover-plus method or by changing the settings), we see the correct exact answer. Is this an OS glitch of some sort? Is there something we should be doing differently?
--
--
To post to this group, send email to tins...@googlegroups.com
To unsubscribe send email to tinspire+u...@googlegroups.com
For more options, visit this group at
http://groups.google.com.au/group/tinspire?hl=en-GB?hl=en-GB
The tns documents shared by group members are archived at
https://sites.google.com/site/tinspiregroup/classroom-news/welcome-abouttime

---
You received this message because you are subscribed to the Google Groups "tinspire" group.
To unsubscribe from this group and stop receiving emails from it, send an email to tinspire+u...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/tinspire/7ae61fb9-a26a-45f6-b1f1-357a55987cb7n%40googlegroups.com.

--
--
To post to this group, send email to tins...@googlegroups.com
To unsubscribe send email to tinspire+u...@googlegroups.com
For more options, visit this group at
http://groups.google.com.au/group/tinspire?hl=en-GB?hl=en-GB
The tns documents shared by group members are archived at
https://sites.google.com/site/tinspiregroup/classroom-news/welcome-abouttime

---
You received this message because you are subscribed to the Google Groups "tinspire" group.
To unsubscribe from this group and stop receiving emails from it, send an email to tinspire+u...@googlegroups.com.

To view this discussion on the web visit https://groups.google.com/d/msgid/tinspire/00a701d7363e%24b3b736c0%241b25a440%24%40optonline.net.

hastern

unread,

Apr 22, 2021, 9:51:23 AM4/22/21

to tinspire

I don't think Float n means what you think it means.

Note the following screenshot, set to Float 6. It still shows 3 sig dig.

Peggy Frisbie

unread,

Apr 22, 2021, 12:40:08 PM4/22/21

to tinspire

Epi -- That's really interesting. Thanks for pointing it out.

Mr. Stern, you've clearly got a point here, although I cannot reproduce your vertex issue; my calculator shows (1234, 1) at the vertex when I am using float 6. I do get (1.23E+3, 1) when I set the graphing display to Float 3.

For many situations, I find that Float n gives n significant digits, but with Float 6 on a graph screen, tracing along eˣ goes from (–13.6, 0.00001) to (–13.9, 9.18981E–7). A quick search online did not give me a definitive answer as to what the Float setting means on this calculator. Can anyone point me to an explanation?

eagl...@duetsoftware.ca

unread,

Apr 22, 2021, 12:55:42 PM4/22/21

to tins...@googlegroups.com

Iirc, Float gives up to n digits of needed, whereas Fix always gives n digits. So with Float 3 you would have 2.1, but with Fix 3 you have 2.10. The real difference is what happens when you have fewer than n digits, but they should act the same if you have more.

Eric

On Apr 22, 2021, at 9:40 AM, Peggy Frisbie <peggyf...@gmail.com> wrote:

To view this discussion on the web visit https://groups.google.com/d/msgid/tinspire/69b49851-89c9-42be-963d-c9d50767b4cbn%40googlegroups.com.

David Young

unread,

Apr 22, 2021, 3:47:37 PM4/22/21

to tins...@googlegroups.com

or maybe Fix 3?

DAY

David Young
Fayetteville
Mathematics - Sciences - Tech
dayo...@gmail.com

http://militantgrammarian.com/DAY/

"Just because it did not happen does not mean it isn't True."
-Some Writer in Fayetteville

Reply all

Reply to author

Forward