These are the images of the graphs I want to know the academic names:

bell-shaped curve upside down bell-shaped curve

I've googled and learnt that their names are Concave Down Curve and Concave Up Curve. However, I want to know if there are any other names for these graphs as I want to use them in a sentence like:

"The sales from 2011 to 2017 resembles a concave down curve with the lowest point being 2015 at 20,356 sales"

Edit 1: Guys, thank you for your inputs. However, my question was not that related to math, but was to find a good descriptive sentence for my IELTS writing. Here is the graph I came across in the test:

bar chart image taken from IELTS Writing task 1 paper

I noticed that, as people get older, women tend to do more exercises, and then less, their trend shapes like a bridge, while a reversion of that can be seen in men. Now, if I were to compare these two trends while trying to sound academic, should I write something similar to the following?

"A demographic trend which resembles a concave down curve can be seen in women's figures while it is the opposite for men's"

Could you guys give me a more well structured and better sentence without sacrificing the "concave down curve or u-shaped curve" because I really want to include those terms.

  • 4
    'U-shaped curve' is standard, but reasonably similar-shaped (in the everyday sense) graphs may be said to 'resemble a parabola etc'. But this is better asked on Mathematics SE. Commented Aug 5, 2017 at 12:53
  • 4
    This question belongs on another site in the Stack Exchange network. Commented Aug 5, 2017 at 12:55
  • 3
    'Inverted U-shaped curve'. 'Concave up' etc are also commonly used, but apply to parts of graphs. See mathsfirst.massey.ac.nz. Commented Aug 5, 2017 at 13:50
  • 4
    They're both parabolas; they're more common of architectural arches than brides. Actual suspension bridges, like the Golden Gate Bridge, have a different curve, known as a a catenary.
    – Dan Bron
    Commented Aug 5, 2017 at 13:54
  • 1
    Concave and convex would be understood by mathematicians. Commented Aug 5, 2017 at 22:37

5 Answers 5


This being sales data and not a pure function, I wouldn't advise using an academic description. I'd expect sales data at a micro-level to move in a geometric manner, due to the nature of communication. The example graphs look polynomial.

If I were instructing someone to draw this graph, I would tell them to draw a parabola whose endpoints approach positive/negative infinity.

Referring to the "low point," I'd call it this valley's local minimum. Unless it was the lowest point in the range, which would be the absolute minimum.

  • parabola is the simplest curve after straight lines, according to Wikipedia.
    – Lambie
    Commented Apr 12, 2021 at 14:49

Positive convexity means concave up. Negative convexity means concave down. The positive and negative refer to the positive/negative value of the rate of change of the function f'. (To understand the meaning rate of change you need to at least do Calculus 1)

It is a commonly used term in finance.

See definitions below:

Investopedia: Convexity

Corporate Finance Institute: Negative Convexity.


Looking at the shape of your graphs, it is best to simply say that the percentage for women increases and then decreases, while that for men decreases and then increases.

  • 1
    That's a bit too generic, it doesn't really describe the gentle rise and fall. I'm sure you can do better.
    – Mari-Lou A
    Commented Aug 6, 2017 at 17:32
  • 1
    Just saying the percentage for women increases then decreases is too vague. Does it dramatically increases, or does it climb steadily but slowly? And by how much? A 2% and a 25% rise both show an increase but only one of them is significant. In the bar chart displayed, the difference between the lowest and the highest percentage of women is just under 6%. As you can see, I used no technical words but the description reflects more accurately the actual graph.
    – Mari-Lou A
    Commented Aug 8, 2017 at 21:21
  • Jasper Loy...poof, gone again.
    – Mari-Lou A
    Commented Aug 24, 2017 at 12:26

The phrase I've seen for the first curve is "Inverted-U Function". Examples are:

Inverted-U Hypothesis
Inverted-U Function

And the second graph is called a "U-Curve":

Midlife Crisis? Or Just Bottoming Out on the U-Curve of Happiness
Happiness, stress, and age: How the U-curve varies across people and places


The curve is called a 'catenary', the curve of a cable or chain suspended at two points, while under the influence of gravity.


  • 2
    The curves OP shows aren't catenaries. Their 'like a bridge' descriptor is somewhat misleading. Commented May 12, 2020 at 15:52

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