Russian Translation(s) & Details for 'quadratic'

English Word: quadratic

Key Russian Translations:

• квадратичный /kvə.drəˈtʲi.tɕ.nɨj/ - [Formal, Mathematical context]

Frequency: Low (This term is primarily used in academic, scientific, or mathematical discussions and is not common in everyday conversation.)

Difficulty: B2 (Intermediate; Requires familiarity with mathematical terminology and basic Russian adjective declensions, suitable for learners with some exposure to technical language.)

Pronunciation (Russian):

квадратичный: /kvə.drəˈtʲi.tɕ.nɨj/

Note on квадратичный: The stress falls on the third syllable ("tʲi"), and the "тʲ" sound is a palatalized 't', which can be challenging for English speakers. Pronounce it with a soft, almost 'ch'-like quality in Russian.

Audio: []

Meanings and Usage:

Meaning 1: Relating to a quadratic equation, function, or anything involving the square of a variable (e.g., in mathematics or algebra)

Translation(s) & Context:

• квадратичный - Used in formal mathematical contexts, such as describing equations or functions where the highest power is two (e.g., in algebra, physics, or engineering discussions).

Usage Examples:

• Решение квадратичного уравнения требует знания дискриминанта.

  Solving a quadratic equation requires knowledge of the discriminant.

• Эта функция является квадратичной и имеет параболическую форму графика.

  This function is quadratic and has a parabolic shape on the graph.

• В линейной алгебре квадратичные формы используются для анализа матриц.

  In linear algebra, quadratic forms are used to analyze matrices.

• Квадратичный член в уравнении определяет его нелинейность.

  The quadratic term in the equation defines its nonlinearity.

• Студенты изучают квадратичные уравнения в курсе высшей математики.

  Students study quadratic equations in their advanced mathematics course.

Russian Forms/Inflections:

"квадратичный" is an adjective in Russian, which means it undergoes declension based on gender, number, and case. It follows the standard pattern for first-declension adjectives. Below is a table outlining its key inflections:

Note: This adjective does not have irregular forms, making it relatively straightforward for learners once basic declension rules are understood.

Russian Synonyms/Antonyms:

• Synonyms:
  • квадратный (more general, often used for "square" in geometry, but can overlap in some mathematical contexts; less precise for equations)
• Antonyms:
  • линейный (linear, as in straight-line relationships)
  • кубический (cubic, referring to third-degree equations)

Related Phrases:

• квадратичное уравнение - A quadratic equation; Used in algebra to describe equations of the form ax² + bx + c = 0.
• квадратичная функция - A quadratic function; Refers to functions like f(x) = ax² + bx + c in mathematical modeling.
• квадратичная форма - Quadratic form; Common in linear algebra for representing bilinear expressions.

Usage Notes:

This translation corresponds closely to the English "quadratic" in mathematical contexts, emphasizing second-degree polynomials. It is strictly formal and academic, so avoid using it in casual conversations. When choosing between "квадратичный" and similar terms like "квадратный," opt for "квадратичный" for precision in algebra. Grammatically, ensure the adjective agrees in gender, number, and case with the noun it modifies, as per standard Russian rules. For example, pair it with neuter nouns like "уравнение" in the neuter form.

Common Errors:

• Confusing "квадратичный" with "квадратный": Learners often misuse "квадратный" (meaning "square" or "squarish") in mathematical contexts. Incorrect: "Квадратное уравнение" (This implies a "square equation," which is not standard). Correct: "Квадратичное уравнение." Explanation: "Квадратичный" specifically denotes second-degree polynomials, while "квадратный" relates to geometric squares.

• Forgetting declension: English speakers might use the base form everywhere, e.g., saying "квадратичный уравнения" instead of "квадратичного уравнения" in genitive case. Correct usage requires proper inflection to match the noun's case.

Cultural Notes:

In Russian-speaking academic circles, terms like "квадратичный" reflect the influence of Western mathematics, particularly from 18th-19th century developments in algebra. While not tied to specific cultural traditions, it underscores Russia's strong emphasis on STEM education, where mathematics is a core subject from an early age, often integrated into national curricula like those in schools or universities.

Related Concepts:

• линейный
• кубический
• полиномиальный