Meaning & use
quadratic
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Meanings
adjectivebefore a nounmathematics
Describing an equation or expression whose highest power of the unknown is two.
Grammar: Almost always placed before a noun: a quadratic equation, a quadratic function.
Patterns
- quadratic equation
- quadratic function
Students learn to solve a quadratic equation by factoring or by using a formula.
The graph of a quadratic function is a curve called a parabola.
She wrote a quadratic expression for the area of the garden.
nouncountablemathematics
An equation or polynomial in which the highest power of the variable is two.
Grammar: Used as a noun in school mathematics: solve the quadratic.
Patterns
- solve a quadratic
- factor a quadratic
The teacher asked us to factor the quadratic on the board.
This quadratic has two real roots.
After rearranging the terms, he had a quadratic to solve.
Word forms
| plural | quadratics |
|---|
Common combinations
- quadratic equation
- The quadratic equation had two solutions, three and negative one.
- quadratic formula
- If it will not factor, use the quadratic formula.
- quadratic function
- A quadratic function produces a U-shaped graph.
- quadratic growth
- The cost showed quadratic growth as the system got larger.
- solve a quadratic
- Can you solve a quadratic by completing the square?
Synonyms and how they differ
- second-degree
- Second-degree is a more descriptive term used in algebra, whereas quadratic is the standard short form in most classrooms.
- squared
- Squared describes one term raised to the power two, while quadratic describes a whole equation or function containing such a term.
Opposites
Word family
- quadrate adjective
- square or nearly square in shape
- quadrant noun
- one quarter of a circle or of a coordinate plane
- quadratically adverb
- in a way that follows a squared relationship
- quadrilateral noun
- a shape with four straight sides
Commonly confused: quadratic or cubic? quadratic or quadruple?
quadratic vs cubic
A cubic equation has its highest power equal to three, while a quadratic has two.
quadratic vs quadruple
Quadruple means four times as much, and is unrelated to the squared power in a quadratic.
Practice
Which of these is a quadratic equation?
Choose one answer.
A quadratic has the unknown raised to the second power at most, as in x^2 - 5x + 6 = 0. The first is linear and the third is cubic.
Make it your own
Write a sentence using “quadratic”, then check it and compare it with the examples above.