# Year 10+ Coordinate Geometry

### Chapters

### The Square Function

# The Square Function

The `square function`

is the function

Here's a table of some values for the square function:

\(x\) | \(f(x)\) |
---|---|

\(-3\) | \(9\) |

\(-2\) | \(4\) |

\(-1\) | \(1\) |

\(0\) | \(0\) |

\(0.5\) | \(0.25\) |

\(1\) | \(1\) |

\(2\) | \(4\) |

\(3\) | \(9\) |

\(\text{elephant}\) | \(\text{elephant}^2\) |

\(\pi\) | \(\pi^2 \approx 9.8696\) |

And here's its graph:

We call graphs with this shape `parabolas`

.

## Properties of the Square Function

Its domain is the set of all real numbers.

Its range is the set of non-negative real numbers: \([0,\infty)\).

Its minimum value is at \((0,0)\). We call this the `vertex`

of the parabola. This is the point where the parbola turns around.

It has no maximum value.

It is increasing for \(x > 0\) and decreasing for \(x

It is symmetric about the \(y\)-axis. If you stick a mirror along the \(y\)-axis, one half of the square function will reflect exactly onto the other half.

It is an even function: \(f(x) = f(-x)\) for all real \(x\).

### Description

A **coordinate geometry** is a branch of **geometry** where the position of the points on the plane is defined with the help of an ordered pair of numbers also known as **coordinates**. In this tutorial series, you will learn about vast range of topics such as Cartesian Coordinates, Midpoint of a Line Segment etc

### Audience

year 10 or higher, several chapters suitable for Year 8+ students.

### Learning Objectives

Explore topics related to Coordinates Geometry

Author: Subject Coach

Added on: 27th Sep 2018

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