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Quadratic Functions: Examples & Formula

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  • 0:00 What Is a Quadratic Function?
  • 0:34 How Do They Look Graphed?
  • 1:19 The Different Ways to…
  • 2:34 The Quadratic Formula
  • 3:14 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Learn what sets quadratic functions apart from all other functions. Learn how you can spot a quadratic just by looking at its graph. Also learn the two formulas that will help you when working with them.

What Is a Quadratic Function?

A quadratic function is a function or mathematical expression of degree two. This means that the highest power of the function is two.

Examples of quadratic functions.
quadratic

All of the examples are of degree two. In other words, their highest power is two. Quadratic functions must have two as their highest power. It cannot be lower or higher. If it's lower or higher, it is no longer a quadratic.

How Do They Look Graphed?

Quadratic functions have a certain characteristic that make them easy to spot when graphed. They will always graph a certain way. Try graphing the function x^2 by setting up a t-chart with -2, -1, 0, 1, 2 to see what you get.

The graph of x squared.
quadratic

This particular shape is called a parabola. Quadratics will always graph into some form of parabola. They can stand upright like x^2 or they could be sideways if the variable is y. They can be located at different spots on the Cartesian plane, but they will always have a porabola.

The Different Ways to Write a Quadratic

The most common way of writing quadratic functions is in the standard form. In standard form, you write the terms in decreasing order such that the term with the highest exponent is first and the constant is last.

Standard form.
quadratic

You will see standard form often. When making calculations on paper, this is the form that is usually given. In this example, a is 1, b is 5, and c is 6. There are, however, other forms.

Another form is called factored form, in which the roots or solutions of the quadratic equation are written as products to be multiplied.

Factored form.
quadratic

All quadratic functions have two roots. The roots can be different or they can be the same. In this example, the two roots are -2 and -3.

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