Talk:Quadratic function

Why _quad_ratic?

Silly question perhaps, but why are they called quadratic? Highest power is _two_, number of terms is _three_; where's the four come from?

It's the same reason that x² is called "x-squared". Back when geometry was all of mathematics, a common problem people wanted to solve was quadrature, i.e. turning things into squares. Algebraically, problems involving squares and turning things into squares are always second power (because the area of a square with side x is x²). So call x² "x-squared" because it is the square associated with x, and call any equation involving this squared quantity a quadratic equation. Similarly, third degree functions are called cubic, rather than "ternary" or some other such -Lethe | Talk 18:06, Aug 22, 2004 (UTC)

Hello Lethe, kindly refer to "Etymology" section of this article for your question. Also Talk pages are not forums. - S L A Y T H E - (talk) 21:08, 24 August 2023 (UTC)

Section ordering.

Would it be an a good idea to move the 'Roots' section below the 'Graph' section in the body.

I think the article would flow better that way and since the 'Graph' section contains the first part of the derivation of the equation for the roots as well. (As I remember them).

I'm asumming the derivation is not spelt out to stop people just copy the page for thier homework. ;-).

I think we should add a new article that discusses quadratic factoring. We also need better organization with this article because the sections are very randomly ordered. After organizing this article, let's add a paragraph about all the methods of factoring. Then we can provide a link to the new article (about factoring), which will go into the whole schmellalagang of factoring in detail. Anyone with me on this?

Matrix formulation

I think you should mention the matrix formulation of multivariate quadratics. Your formula is equivilant to $\mathbf {x} ^{T}\mathbf {A} \mathbf {x} +\mathbf {b} ^{T}\mathbf {x} +c$, $\mathbf {A}$ is a symetric 2 by 2 matrix, $\mathbf {b}$ and $\mathbf {x}$ are 2-vectors, and $c$ is a scalar. I think the vertex is where the gradient ($2\mathbf {A} \mathbf {x} +\mathbf {b}$) is zero: so $2\mathbf {A} \mathbf {x} =\mathbf {b}$, which can be solved easily by Cramers rule. The hessian matrix is everywhere $2\mathbf {A}$, which is the shape operator of the plot-surface at the vertex. The quadratic can be rotated by a givens rotation to make $\mathbf {A}$ into a diagonal matrix (call it $\mathbf {D}$) and put the quadric in a standard orientation. I think the elements of $\mathbf {D}$ are half the the principle curvatures of the plot at the vertex. I would add to the page directly, but I dont have time to double-check my facts first. The page probably should list the fundamental forms (I think they turn out to be very simple for quadratics).

Yeah I agree. ~Claire — Preceding unsigned comment added by 75.118.134.25 (talk) 00:16, 13 December 2012 (UTC)

It needs to be $2\mathbf {A} \mathbf {x} =-\mathbf {b}$. Dunbur (talk) 00:12, 12 October 2018 (UTC)

Java render

In package java.awt.geom, there are classes QuadCurve2D, QuadCurve2D.Double, QuadCurve2D.Float. We can use them to draw a quadratic curve. In order to construct such an object, we need two points on the curve, and one control point. What does this control point mean? Jackzhp 19:09, 27 December 2006 (UTC)

Doesn't the documentation say what it means? But it probably has the obvious meaning: the line from this point to either of the other points is a tangent to the curve at that point. See the stuff on quadratic curves in the Bézier curve article. --Zundark 10:03, 28 December 2006 (UTC)

JDK's documentation doesn't say anything about the control point. However, your information gives the way to understand the stuff. Thanks. Furthermore, if we know y=ax^2+bx+c goes through point A & B, we need a formula to get the control point C. Conversely, if we know the point A,B, & C, we should have a formula to find a,b,& c. Can somebody post the fomulas here?Jackzhp 01:42, 30 December 2006 (UTC)

What makes you think the curve is given by $y=ax^{2}+bx+c$? The way you describe the classes, the axis of the parabola needn't be vertical. --Zundark 18:47, 30 December 2006 (UTC)

Thanks for your responding. ok. suppose the curve is ax^2+bxy+cy^2+dx+ey+f=0 goes through point A(xA,yA) & B(xB,yB). we need a formula to get the control point C(xC,yC). then we can use these three points to draw the segment between point A&B. What is the formula? Conversely, if we know the points A,B,C, we need the formula to find a,b,c,d,e,f. What is this formula again? Thanks. Jackzhp 21:11, 31 December 2006 (UTC)

Explanation of A and other variables

Nowhere in this article does it explain what the variables A, B, C, D, E, and F are for the Bivariate quadratic function. 69.119.189.202 23:27, 21 May 2007 (UTC)

Vertex

Gah! I went around thinking that the vertex of a parabola is (h, -k) because of this article. The vertex should be just (h, k) Am I wrong??68.149.9.65 00:27, 19 September 2007 (UTC)

The vertex of a parabola is (h, k).156.34.177.71 17:29, 21 October 2007 (UTC)

Merge proposal with Quadratic polynomial

The following discussion is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

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• Support. Move relevant content from Quadratic polynomial into Quadratic equation and keep this one as the master. DVdm (talk) 20:03, 12 October 2011 (UTC)

The proposal seems to be to merge quadratic function with quadratic polynomial, which apparently would not affect quadratic equation.Anythingyouwant (talk) 07:33, 11 September 2013 (UTC)

I.m.o. best to move function and polynomial together into quadratic equation. - DVdm (talk) 15:18, 15 September 2013 (UTC)

It might be best to start by merging two of those articles, and then we can start a discussion about merging with the third. Can we start by merging poly and func? Wikipedia isn't really set up to merge three at once. Plus, I think quadratic equation is already pretty long.Anythingyouwant (talk) 15:22, 15 September 2013 (UTC)

• In the Quadratic polynomial article "polynomial" takes on various meanings, including polynomial expression, polynomial equation, and polynomial function. What is the specific "relevant content" proposed to be moved / merged? Thelema418 (talk) 04:16, 7 April 2012 (UTC)

• I support the proposal that this article be merged with Quadratic polynomial. The material is closely related, and the articles are short enough to allow a single merged article.Anythingyouwant (talk) 14:21, 15 September 2013 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

Restoring a curve having three distinct points

We should say that it is possible to restore a quadratic curve having three disticnct points (and to explain how it can be done). VictorPorton (talk) 21:14, 26 December 2011 (UTC)

Do you have any particular book (author, title, publisher, isbn, page) in mind that we can use as a source? - DVdm (talk) 22:34, 26 December 2011 (UTC)

Sockpuppetry

This article has had several edits from an IP address used by blocked user Glkanter that were reverted as being vandalism. Please keep an eye out for further abuse. Also see: Wikipedia:Sockpuppet investigations/Glkanter/Archive, Wikipedia:Sockpuppet investigations/Glkanter and Wikipedia:Arbitration/Requests/Case/Monty Hall problem#Glkanter banned. --Guy Macon (talk) 08:23, 22 April 2012 (UTC)

Discussion about inappropriate external link

Discussion about my revert of this edit at Talk:Quadratic_equation#Inappropriate_external_link. - DVdm (talk) 18:54, 17 May 2012 (UTC)

Improving last September's merge

Last September's merge seems to have simply copy-and-pasted the other article into the bottom of this one, leaving a lot of redundancy. I'm going to complete the merge by cutting from the bottom whatever is better covered earlier, and moving the better things in the lower part to the upper part. Please bear with me if this process creates some temporary roughness, which should only last for a few minutes. 208.50.124.65 (talk) 17:01, 13 August 2014 (UTC)

Clarifying univariate vs. multivariate

It looks like the article began in terms of only the univariate case, and then the multivariate case was added here and there without adding the qualifier "univariate" to the univariate sections. I'm going to work on it to make it flow better in this regard. Loraof (talk) 14:37, 17 October 2014 (UTC)

"Declivity"?

WTF is "declivity", as in

The coefficient b alone is the declivity of the parabola as y-axis intercepts

???

The definitions I find say "downward slope"; does that just mean the slope time -1? Or should this just say "slope at the y intercept"? In any case, "declivity" doesn't really seem to be a math term, as far as I can tell, e.g. wiktionary lists it as a geology term:

http://en.wiktionary.org/wiki/declivity — Preceding unsigned comment added by 2601:B:AD00:8B31:D03F:EBDF:2B35:BCD7 (talk) 14:28, 9 April 2015 (UTC)

Are all graphs of quadratic functions parabolas?

If all graphs of quadratic functions are parabolas, then that would be a very important information to add to the article (assuming there are citations). - S L A Y T H E - (talk) 16:06, 4 January 2023 (UTC)

This is already in the article: Regardless of the format, the graph of a univariate quadratic function is a parabola. D.Lazard (talk) 17:16, 4 January 2023 (UTC)

This article probably needs some protection

Due to recurring vandalism, do you people consider semi-protecting the article? - S L A Y T H E - (talk) 00:24, 14 June 2024 (UTC)

It doesn't seem necessary to me. YMMV. –jacobolus (t) 02:11, 14 June 2024 (UTC)

Bi-Variate Min/Max

In the closing bi-variate section it presents cases of the min/max y/x values of a quadratic function without proof or reference. How are the conditions presented derived? It states "Such a function describes a quadratic surface." - this is incorrect as it defines a curve and not a surface. The standard convention for the 2-variable conic function is Q=Ax^2+Bxy+Cy^2+Dx+Ey+F=0, which differs from what is presented. Thus, I would doubt the presented min/max results without proof or reference as it is all too easy to get the coefficients mixed up.

Indeed - the more I read the closing min/max section on the bi-variate form the more confused I get. The equation describes a conic "curve" and not a surface as previously stated and yet the section states "its graph forms a hyperbolic paraboloid.". A paraboloid is a 3D (x,y,z) surface and not a 2D (x,y) curve. The more I read this section the more I conclude it is utter nonsense. — Preceding unsigned comment added by 81.187.174.43 (talk) 08:29, 25 September 2024 (UTC)

The lead needs substantial reworking to make it more broadly understandable

This article is a technical article. A lot of useful guidance material is provided at WP:Make technical articles understandable. This guidance begins by stating that the lead section should be understandable to the widest possible audience, and points to specific guidance at WP:LEAD.

The lead section in this article fails when assessed against the criteria provided in this guidance material. The lead section should be reworked so it gets closer to meeting the criteria.

The first paragraph in the lead section is largely about the distinction between the function and the polynomial, even commenting on historical aspects of elementary courses in this subject. It is particularly poor when assessed against the relevant criteria. It should be reworked with some urgency. Dolphin (t) 11:15, 11 October 2024 (UTC)

Because of the title, the "widest possible audience" consists for this article, of people who do not need to open Function (mathematics) to understand any sentence containing the word "function". Nevertheless, the lead could certainly be improved from this point of view, without loss of accuracy. If you have an idea for that, please propose here a new version of the first paragraph in order to discuss whether if it improves the current lead. D.Lazard (talk) 12:01, 11 October 2024 (UTC)

Thank you for making your changes. I particularly like your new first paragraph. It is exactly what I would have proposed.

The lead section is expected to summarise material that is provided in greater depth in the body of the article. I would remove the paragraph “Before the 20th century ...” and rely entirely on whatever is said on this matter in the body of the article. This historical note is unlikely to be of value to readers who are reading the article to introduce themselves to quadratic functions or to refresh their memory of the topic.

Similarly I consider it inappropriate for the lead section to contain detail about quadratic functions with two variables and three variables. Such detail should be left for the body of the article. I think it would be sufficient to end the lead section with a short summary such as “Quadratic functions can have one, two, three or more variables.” Dolphin (t) 12:41, 11 October 2024 (UTC)

IMO, the explanation of the difference between a quadratic function and a quadratic polynomial must be kept in the lead, since, otherwise many readers would be confused by the unavoidable distinction between these two concepts. Othewise, I agree that some detaild may be removed from the lead, but the distinction between quadrics and quadratic polynomials must be kept for avoiding common confusions. D.Lazard (talk) 14:49, 11 October 2024 (UTC)

I tried to tighten this. I think belaboring this in the lead section is likely to be distracting for less-technical readers and not that helpful for more technical readers. –jacobolus (t) 16:48, 11 October 2024 (UTC)