What is Delta? - Definition & Concept

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  • 0:01 What Does Delta Look Like?
  • 0:19 What Does Delta Mean?
  • 1:23 Delta as the Difference
  • 2:19 Delta as the Discriminant
  • 3:16 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.

Delta is a letter of the Greek alphabet with several different mathematical meanings. Learn about the functions of delta, what it looks like, and how you can use delta in your mathematical expressions in this lesson.

What Does Delta Look Like?

Delta is the fourth letter in the Greek alphabet. It is comparable to our letter D. Like the D in our alphabet, delta can be lowercase or uppercase. Each looks different from the other and both are used differently:


What Does Delta Mean?

Uppercase delta has two different mathematical meanings. Both meanings begin with the letter D just like the Greek letter, which should help you remember them:

  1. Difference is the most common meaning of the uppercase delta. It is simply the difference, or change, in a certain quantity. When we say delta y, for example, we mean the change in y or how much y changes.
  2. Discriminant is the second most common meaning of the uppercase delta. The discriminant is found in the quadratic formula and determines the number of solutions a particular quadratic equation has.

The lowercase delta is seen more often in calculus. Its meaning also starts with the letter D: distance from the limit, in calculus. It is used when calculating limits in calculus. The first two meanings are the most common and have formulas associated with them. We will discuss those two here and show you the formulas. The third meaning is strictly that, a meaning, and has no associated formula. Because there is no formula to show, we won't go further into that meaning.

Delta as the Difference

Delta's most common meaning is that of difference or change in something. Usually, you will hear or see it as delta y, delta t, delta x, etc. Delta occurs most often when you are working with speed or acceleration or anything that changes. The slope of a line, for example, can be spoken of as delta y over delta x. From the slope we can get a formula for delta:


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