1. Those are already in it. The discriminant is termed "Delta" Portugese.

C17 gives the value of the discriminant. ("O Valor de Delta é") [It does not explain about the number of roots, but does give them in some fashion]
C19 gives either the roots or the intersection points of the parabola with the X-Axis (when Y=0) [This is a style point I mentioned earlier]
C21 gives whether the parabola is concave up or down
C24 gives info on the Y-intercept (when X=0)

My post#12 makes some additional comments as does the post #10 to clean it up a little.

Steve

2. I have taken a crack at making some changes as suggested by Steve and others. In particular, the attached (excuse my changing the name of the file) reflects the following:
- did Steve's first 2 changes to get rid of "spurious" dots when a=0 (see below for 3rd suggested change)
- added a calculation for the vertex and displayed that on the graph as part of Series 2 (the "critical" points of the parabola) and as its own "orange box"
- for non-Portuguese speakers, I added some "titles" and explanations around each of the "control" boxes; in doing this, I tried to be consistent with the fine distinction that Steve made re: the quadratic function vs the parabola
- widen one of the columns so that the entire x-intercept info is shown when there are 2 roots to the quadratic

What I couldn't do bcs of some protection (at least that's my poor understanding of the error msg when I tried to edit a formula or change some other things):
- make Steve's 3rd change (I believe that should have been for the x-intercept, not y-intercept per the comment; the y-intercept does show regardless of whether the function is linear or quadratic which is why I agree the x-intercept should also be shown regardless of function type)
- change the title box at top to display the Portuguese version of "Quadratic Function/Parabola" and an English translation of both: something like "Quadratic Function/Parabola" in Portuguese followed by " - Quadratic Function/Parabola" in English (although the latter may not really be necessary since the Portuguese is obvious at least to this English-only speaker

What might also be useful, since I teach it, is to show non-real roots for the Quadratic when applicable (which would really require a distinction between roots of an equation and x-intercepts of a parabola). This might be useful since the Discriminant value is given regardless of the type of roots.

One other thing: I somehow inadvertently turned off the display of the x-values on the graph of the Series 2 points. I couldn't find how to get them back. But I decided that this wasn't so bad: less clutter when the points are close together and the values are given in the orange boxes anyway.

Someone else can take a turn on the next iteration.

Fred

3. The "protection" is data validation which can be removed.

The 2 "non-real roots" (ie the complex numbers) would be in the form q + ri and q - ri [Note: I changed the typically used a+bi to avoid confusion with the a & b that are already being used for the quadratic]. The values can be calculated from existing named formulas if desired.
q = -coef_b /2/coef_a
r = sqrt(-delta)/2/coef_a
delta (as mentioned before) is the discriminant = coef_b^2 - 4*coef_a*coef_c
and i represents the Sqr Root of -1

Steve

4. OK. I guess I'll do the next iteration.

With Steve's hint on the "protection," I was able to do the two items from my previous post that I said I couldn't do (removed the Data Validation and then restored it when done although I don't quite understand what the Custom Validation of <>123&"---" does):
- the x-intercept is calculated as I mentioned (it is not the y-intercept)
- the title is enhanced (I looked up the Portuguese for "Parabola" - if it's wrong, pls correct it)

While I know how to calculate the coefficients of a+bi (or a+bj for electrical engineers, or whatever letters you want), I did not want to start playing with the spreadsheet. It would probably take a little work and I just didn't have any more time for now.

I also fixed my "American" notation of the coordinates of a point, where I had added that, to reflect the original Portugues (using a ; separator between the x-coordinate and y-coordinate).

Steve-I never use a stacked division for something like -coef_b/2/coef_a since I never thought that way. Without it, you need parens for the (2*coef_a), which may easily be forgotten. I like your way better although I've never heard the Quadratic Formula taught that way (you can see all kinds of YouTube tutorials that use 2*coef_a for the divisor).

Fred

5. OK. I did one more iteration.

Changes from the last version:
- for purposes of teaching about parabolas, a concept called the Axis of Symmetry (AoS) exists. It cuts the parabola symmetrically in half. So if you can graph the parabola on one side of the AoS, the other side is a mirror reflection. I added an "orange control" box for this and also showed it on the graph (as long as coef_a <> 0 resulting in a linear function)
- depending on the value of coef_a and the min/max x-values for the graphing window, there may not be any points on the parabola. The original used a fixed set of x-values for the parabola's graph (-100 to +100 in increments of 0.5). For coef_a <1, this may not show anything. So I made the x-values for the parabola dependent on the graphing window. I'm not totally happy with this but it will work for my purposes. One small problem is that the red dots (representing the values to be graphed for the function) clump up around the parabol's vertex.
- added in the possibility of complex roots for delta/discriminant < 0 (in English)
- emphasized the case of one unique root (one x-intercept) (unfortunately, this is a mix of Portugues and English)
- other minor editorial changes

With this, I think I'm finished. My goal was to take the excellent post (which I could never have done) and morph it into something I could use for teaching. And my students will get some Portuguese as a bonus.

Fred

6. found one small error in how complex roots are presented. fixed that.

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