Etymology
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quadratic (adj.)

1650s, "square," with -ic + obsolete quadrate "a square; a group of four things" (late 14c.), from Latin quadratum, noun use of neuter adjective quadratus "square, squared," past participle of quadrare "to square, make square; put in order," related to quadrus "a square," quattuor "four" (from PIE root *kwetwer- "four"). In mathematics by 1660s; the algebraic quadratic equations (1680s) are so called because they involve the square and no higher power of x.

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Definitions of quadratic
1
quadratic (n.)
an equation in which the highest power of an unknown quantity is a square;
Synonyms: quadratic equation
quadratic (n.)
a polynomial of the second degree;
Synonyms: quadratic polynomial
2
quadratic (adj.)
involving the second and no higher power of a quantity or degree;
quadratic equation
From wordnet.princeton.edu