# Formulas, graphs & relations » Power relation

## Contents

1. General2. Formula

3. Graph

## 1. General

A power relation(ship) corresponds to a formula with a power in it. You can use these formulas for lines that increase very fast. For example, the height of a rocket that is being launched or the time it takes to crack a password.

## 2. Formula

The formula is always of the type `y` = `a` · `x`^{n}.

Examples are `h` = –10 · `x`^{8} en `a` = 3`b`^{5}.

The formula `y` = 7`x`^{2} is a quadratic formula and a power formula.

With `h` = –10`x`^{4} + 3`x`^{3} – 5`x`^{2} + 2`x` + 3 you have a *polynomial* in stead of a power formula. In this case a polynomial to the fourth degree.

Note:

When substituting `x` for a negative number in a power, you will get brackets around the negative number!

*Example*

Given is the following formula `y` = 7`x`^{4}.

Calculate `y` when `x` = –3.

Answer: `y` = 7(–3)^{4} = 7 · 81 = 567

## 3. Graph

The graphs corresponding to power relations have different shapes.

The shape depends on a positive or negative number in front of `x` and on an odd or even exponent in the formula.

y = px^{even} |
y = px^{odd} |

y = nx^{even} |
y = nx^{odd} |