quadratic equation

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Explanation of "Quadratic Equation"

Definition: A quadratic equation is a type of mathematical equation where the highest power of an unknown variable (usually represented by the letter ( x )) is a square. This means that ( x ) is raised to the power of 2. The general form of a quadratic equation looks like this:

Usage Instructions:

You use the term "quadratic equation" when discussing mathematics, particularly in algebra. It is important to know how to identify a quadratic equation and how to solve it.

Example:

Here’s a simple example of a quadratic equation: [ 2x^2 + 3x - 5 = 0 ]

Advanced Usage:

In more advanced mathematics, quadratic equations can be solved using various methods, such as: - Factoring: Breaking down the equation into simpler expressions. - Completing the square: Rearranging the equation to form a perfect square trinomial. - Quadratic formula: Using the formula ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ) to find the values of ( x ).

Word Variants:

• Quadratic (adjective): Describing something that relates to or is in the form of a quadratic equation (e.g., "quadratic function").
• Quadratics (plural noun): Referring to multiple quadratic equations or concepts.

Different Meanings:

In different contexts, "quadratic" might refer to things related to squares in geometry, or it might describe functions that graph as parabolas (U-shaped curves).

Synonyms:

• Second-degree equation (another term for quadratic equation).
• Polynomial equation of degree 2.

Idioms and Phrasal Verbs:

There are no specific idioms or phrasal verbs directly related to "quadratic equation," but you might hear phrases like "solve the equation" or "graph the function" in mathematical discussions.

Conclusion:

Understanding quadratic equations is fundamental in algebra, and they appear in many real-world applications, such as physics, engineering, and economics.

Academic

Noun

1. an equation in which the highest power of an unknown quantity is a square

Synonyms

• quadratic