quadratic function

USAGE SUMMARY

"quadratic function" is correct and usable in written English.
You can use it when referring to an equation in two variables--usually represented by x and y--where the highest power of the variable is two (e.g. y = 2x2 + 3x + 4). For example, "The quadratic function y = 2x2 + 3x + 4 has two solutions."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

59 human-written examples

The quadratic function satisfies the functional equation.

Journal of Inequalities and Applications

for all then is a quadratic function.

Journal of Inequalities and Applications

end{aligned} This is a quadratic function.

Advances in Difference Equations

Then there exists a quadratic function such that (3.26).

Journal of Inequalities and Applications

We also presented the properties of the obtained quadratic function.

Journal of Inequalities and Applications

For each, define a quadratic function in as follows: (3.5).

Fixed Point Theory and Applications

Then there exists a unique quadratic function satisfying (2.4).

Journal of Inequalities and Applications

That is, every solution of (1.2) is a quadratic function.

Journal of Inequalities and Applications

Let be a quadratic function such that (2.87).

Journal of Inequalities and Applications

It can be described by a quadratic function.

EURASIP Journal on Advances in Signal Processing

Finally, to prove the uniqueness of the quadratic function subject to (3.4), assume that there exists a quadratic function which satisfies (3.4).

Journal of Inequalities and Applications

Expert writing Tips

Best practice

When modeling real-world phenomena, consider whether a "quadratic function" accurately represents the relationship between variables, particularly when relationships are non-linear but have a clear maximum or minimum.

Common error

Do not assume a relationship is "quadratic" simply because it curves; ensure the relationship follows the algebraic form of a quadratic equation (ax² + bx + c) and that fitting a linear function isn't more appropriate.

Linguistic Context

The phrase "quadratic function" functions as a noun phrase, typically used to identify and describe a specific type of mathematical function. Ludwig AI confirms its grammatical correctness and common usage in various contexts.

Expression frequency: Very common

Frequent in

Science

98%

Formal & Business

1%

News & Media

1%

Less common in

Academia

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

The term "quadratic function" is a common and grammatically correct noun phrase used to describe a specific type of mathematical function, as validated by Ludwig. It primarily serves to define and categorize mathematical concepts, particularly in scientific and academic contexts. The phrase's formality reflects its prevalent use in specialized fields, emphasizing its precise technical meaning. As per Ludwig's analysis, while predominantly found in scientific literature, there are occasional appearances in formal business and news media, affirming its consistent, albeit less frequent, usage across varied domains. To avoid misuse, it's crucial to ensure that the described relationship strictly adheres to the algebraic form of a quadratic equation.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

polynomial of degree two

Specifies the degree of the polynomial more formally.

function defined by a quadratic

Highlights the definition aspect using a quadratic expression.

second-degree polynomial

Refers to the polynomial's highest degree, emphasizing the algebraic structure.

parabolic function

Focuses on the shape of the graph produced by the function.

curve described by a second-degree polynomial

Focuses on the geometric representation of the quadratic function.

squared function

Highlights the squaring operation as the dominant feature.

equation of degree two

Emphasizes the equation aspect, focusing on finding solutions.

function with a square term

Describes the function based on its most prominent term.

second-order function

Uses "order" to refer to the highest derivative or power involved.

expression involving x squared

Describes the function in terms of its algebraic components.

FAQs

How do I correctly use "quadratic function" in a sentence?

Use "quadratic function" when describing a mathematical function where the highest power of the variable is two. For example, "The trajectory of the ball can be modeled by a "quadratic function"".

What are some alternatives to "quadratic function"?

Depending on the context, you could use alternatives such as "second-degree polynomial" if you're emphasizing the algebraic structure, or "parabolic function" if you're referring to its graphical representation.

Is it always appropriate to model data with a "quadratic function"?

No, a "quadratic function" is suitable when the data exhibits a non-linear relationship with a clear maximum or minimum. If the relationship is approximately linear or follows a different curve, other functions might be more appropriate.

What's the difference between a "quadratic function" and a linear function?

A "quadratic function" involves a variable raised to the power of two (x²), resulting in a curved graph (parabola). A linear function only involves variables raised to the power of one (x), producing a straight line graph. For example, a quadratic function is like y = x² + 2x + 1, while a linear function is like y = x + 1.