# incorrect rounding on a graph page

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### Peggy Frisbie

Apr 20, 2021, 3:53:06 PMApr 20
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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?

### John Hanna

Apr 20, 2021, 7:41:37 PMApr 20

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

Sent: Tuesday, April 20, 2021 3:53 PM
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?

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image001.png

### Peggy Frisbie

Apr 21, 2021, 5:56:14 AMApr 21
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

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Apr 21, 2021, 10:29:29 AMApr 21
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!

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

### Peggy Frisbie

Apr 21, 2021, 1:39:10 PMApr 21
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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:
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

Apr 21, 2021, 10:04:57 PMApr 21
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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?
> Of *Peggy Frisbie
> *Sent:* Tuesday, April 20, 2021 3:53 PM
> *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?
>
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### Karen Campe

Apr 21, 2021, 11:57:33 PMApr 21
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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

Apr 22, 2021, 5:17:08 AMApr 22
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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

Apr 22, 2021, 9:39:58 AMApr 22
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

Sent: Tuesday, April 20, 2021 3:53 PM
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?
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### hastern

Apr 22, 2021, 9:51:23 AMApr 22
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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

Apr 22, 2021, 12:40:08 PMApr 22
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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

Apr 22, 2021, 12:55:42 PMApr 22
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:

﻿

### David Young

Apr 22, 2021, 3:47:37 PMApr 22
or maybe Fix 3?

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