quadratically

8.6

In a way that changes with the square of another number

adverb
/kwɒdrəˈtɪkli/

Specialized

: cuadráticamente

As the size of the square increases, its area changes quadratically, illustrating how area is related to the square of the side length.
quadratically stabilizable

And does that scale linearly or quadratically with a?

Examples

In physics, the energy stored in a spring increases quadratically with the displacement from its rest position.
This effect arises because the maximum-angular-momentum vibrational states have energies proportional to J, whereas rotational energies depend quadratically on J.

Academic text (2006)
In fact, the time gap is scales quadratically with the space gap.
And notice that it contains the edge sizes quadratically, so it's proportional to some area in there.
And this number explodes quadratically very quickly.
A simple case would be rho squared, an energy which increases quadratically away from the origin.
Indeed, their complexity increases quadratically as the number of streamlines increases.

Academic text (2016)
By Lemma 2, the original system (10) is quadratically stabilizable.

Academic text (2010)
By contrast, the SD-standardized selection gradient and the selection intensity, or the proportional selection differential, are shown to increase approximately linearly and quadratically with p, respectively.

Academic text (2012)
A simple example is provided by the analysis of three braids, which confirms a prediction by Eugene N. Parker of the University of Chicago that magnetic energy grows quadratically in time due to random braiding.

Academic text (1996)

Surface Forms

quadratically positive

Morphology

quadratically = quadratic (semi-transparent) = quadrat + ic + ly

The adverb is formed regularly from the specialized adjective 'quadratic', but the mathematical sense may not be fully predictable for all learners.

Etymology

The word quadratically comes from the Latin root quadr-, meaning 'four', and it is the same root you see in quadruple. Think of 'four' as a square: to change quadratically is to change 'as the square' of another number, so if one thing doubles, a quadratically changing thing becomes four times larger.