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Quadratic Meaning: Definition, Examples, and Translations

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quadratic

[kwษ’dหˆrรฆtษชk ]

Definitions

Context #1 | Adjective

mathematics expression

The term 'quadratic' refers to a polynomial of degree two. Quadratic equations take the standard form axยฒ + 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 axยฒ + 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

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Interesting Facts

Mathematical Significance

  • Quadratic equations can have zero, one, or two solutions, which can be found using the quadratic formula: x = (-b ยฑ โˆš(bยฒ - 4ac)) / 2a.
  • They are graphed as parabolas, which are U-shaped curves that can open upwards or downwards, depending on the sign of 'a'.
  • Quadratics are fundamental in various fields, including physics, engineering, and even finance, to model behaviors such as projectile motion.

Cultural Impact

  • Many artists and designers use quadratic functions in modern digital art and architecture to create smooth curves and shapes.
  • In popular culture, quadratic equations occasionally appear in movies and media focusing on characters overcoming math-related challenges, such as in 'Good Will Hunting'.

Historical Figures

  • The Persian mathematician Al-Khwarizmi wrote influential works in the 9th century, contributing to the foundation of algebra that includes quadratic equations.
  • Renรฉ Descartes' work on coordinate geometry in the 17th century revolutionized the approach to solving these equations, linking geometry and algebra.

Physics and Science

  • Quadratic functions often describe trajectories in physics, such as the path of thrown objects or the shape of certain waves.
  • In economics, they can model profit maximization and cost minimization, providing insight into various business scenarios.

Origin of 'quadratic'

Main points about word origin

  • The term 'quadratic' comes from the Latin word 'quadratus', meaning 'square'.
  • Its first recorded use in English dates back to the late 16th century, reflecting the growing interest in algebra at the time.

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.