This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics
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)
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 , is a symetric 2 by 2 matrix, and are 2-vectors, and is a scalar. I think the vertex is where the gradient () is zero: so , which can be solved easily by Cramers rule. The hessian matrix is everywhere , which is the shape operator of the plot-surface at the vertex. The quadratic can be rotated by a givens rotation to make into a diagonal matrix (call it ) and put the quadric in a standard orientation. I think the elements of 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).
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? Jackzhp19:09, 27 December 2006 (UTC)[reply]
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. --Zundark10:03, 28 December 2006 (UTC)[reply]
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?Jackzhp01:42, 30 December 2006 (UTC)[reply]
What makes you think the curve is given by ? The way you describe the classes, the axis of the parabola needn't be vertical. --Zundark18:47, 30 December 2006 (UTC)[reply]
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. Jackzhp21:11, 31 December 2006 (UTC)[reply]
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??68.149.9.6500:27, 19 September 2007 (UTC)[reply]
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.
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)[reply]
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)[reply]
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)[reply]
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.
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)[reply]
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)[reply]
"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:
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)[reply]
