This section focuses on the key features and methods for working with linear graphs. It demonstrates how to sketch graphs from rules, derive rules from graphs, and calculate key features such as the ...

A mathematical function is a formula that takes an input, x, applies a set of calculations to it, and produces an output called y. By calculating a function at a large number of set intervals, it is ...

Plotting a graph takes time. Often mathematicians just want to know the key features. These are: shape, location and some key points (such as where the graph crosses the axes or turning points).

First we need to complete the square to get the coordinates of the turning point. \(y = {x^2} + 2x + 3\) \(y = {(x + 1)^2} - 1 + 3\) \(y = {(x + 1)^2} + 2\) Therefore ...