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Quadratic: meaning, definitions and examples

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quadratic

 

[ kwɒdˈrætɪk ]

Adjective / Noun
Context #1 | Adjective

mathematics expression

The term 'quadratic' refers to a polynomial of degree two. Quadratic equations take the standard form ax² + bx + c = 0, where a, b, and c are coefficients, and a is not zero. These equations can model various real-world situations, such as projectile motion and the area of a square. Solving quadratic equations often involves methods such as factoring, completing the square, or using the quadratic formula. The function represented by a quadratic equation produces a parabolic graph.

Synonyms

biform, second-degree.

Examples of usage

  • The quadratic formula is used to find the roots of the equation.
  • She applied the quadratic method to solve the problem.
  • The quadratic expression can be simplified further.
Context #2 | Noun

mathematics equation

A quadratic refers specifically to a polynomial equation of the second degree. It usually consists of three terms and is expressed in the format ax² + bx + c = 0. Quadratics are fundamental in algebra and are studied in high school mathematics. Solutions to quadratics are called roots, which can be real or complex numbers depending on the discriminant. The graphical representation of a quadratic is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'.

Synonyms

quadratic function, second-degree polynomial.

Examples of usage

  • The roots of the quadratic can be found using various methods.
  • In mathematics, quadratics present critical concepts for advanced studies.
  • Understanding the properties of quadratics is essential for calculus.

Translations

Translations of the word "quadratic" in other languages:

🇵🇹 quadrático

🇮🇳 द्विघातीय

🇩🇪 quadratisch

🇮🇩 kuadratik

🇺🇦 квадратний

🇵🇱 kwadratowy

🇯🇵 二次の

🇫🇷 quadratique

🇪🇸 cuadrático

🇹🇷 ikincil

🇰🇷 이차의

🇸🇦 ثنائي

🇨🇿 kvadratický

🇸🇰 kvadratický

🇨🇳 二次的

🇸🇮 kvadraten

🇮🇸 tvífaldur

🇰🇿 еквадратты

🇬🇪 კვადრატული

🇦🇿 kvadrat

🇲🇽 cuadrático

Etymology

The word 'quadratic' originates from the Latin word 'quadratus', meaning 'square'. This is fitting, as quadratic equations often involve the square of a variable. The use of the term can be traced back to the 17th century in mathematics, particularly in the study of polynomial equations. The appreciation of quadratics developed alongside algebra itself. Over centuries, mathematicians have refined methods for solving these equations, leading to the modern quadratic formula. Thus, quadratics play a crucial role in algebraic education, appearing in various applications from engineering to economics.

Word Frequency Rank

Ranked #11,240, this word falls into high-advanced vocabulary. It appears less frequently but is valuable for expressing precise meanings in specific contexts.