46 lines
1.3 KiB
Markdown
46 lines
1.3 KiB
Markdown
---
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title: Absolute Value
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---
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## Absolute Value
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Absolute value is the non-negative value of a number.
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You can think of a number's absolute value as its distance from zero.
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It can be defined as,
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![img](https://latex.codecogs.com/gif.latex?%5Cdpi%7B120%7D%20%5Clarge%20y%20%3D%20%5Cleft%20%7C%20x%20%5Cright%20%7C%20%3D%20%5Cleft%5C%7B%5Cbegin%7Bmatrix%7D%20x%20%26%20for%20%5C%2C%20x%20%5Cgeq%200%20%5C%5C%20-x%20%26%20for%20%5C%2Cx%20%3C0%20%5Cend%7Bmatrix%7D%5Cright.)
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<img src="https://upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Absolute_value.svg/2000px-Absolute_value.svg.png" width="300">
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The absolute value of a quantity x is denoted by |x| (the quantity is enclosed between two vertical bars).
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Here you can see that in the graph of y = |x|, if -2 is input in to the function, 2 is the result. This is because -2 has a distance of 2 from zero. The absolute value of a number can never be negative.
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### Examples
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* **Simplify |-5|**
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|-5| = 5
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* **Simplify |0(5)|**
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|0(5)| = |0| = 0
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* **Simplify -|-1|**
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-|-1| = -(1) = -1
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* **Simplify |-5(-3) + 1|**
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|-5(-3) + 1| = |15 + 1| = |16| = 16
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* **Simplify |8|**
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|8| = 8
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* **Simplify |(-5)^3|**
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|-125| = 125
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#### More Information:
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<a href='http://www.purplemath.com/modules/absolute.htm "Absolute Value"' target='_blank' rel='nofollow'>Absolute Value</a>
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