# Graphs

Source: https://projectgcse.co.uk/maths/algebra/graphs

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Many algebraic expressions can be interpreted as graphs. Each expression will have a different graph. The shape of the graph can be found from the equation.

**Linear Equations**
The graph made from a linear equation would give a straight line graph. Linear equations are written in the form y = mx + c. From this you can see that the m represents the gradient of the graph and that c shows the point where the graph crosses the y-axis. Here are some examples:

| y = x | y = 2 | x = -6 | y = 2 - 2x |
| --- | --- | --- | --- |

**Quadratic Equations**
These graphs are n or u shaped curves, or parabolas. They all have an axis of symmetry. The equation for these graphs are in the form y = ax2 + bx + c. This means the highest power would be x2. Below are some examples:

| y = x2 | y = -x2 | y = x2 - 8 | y = ( x + 6 )2 |
| --- | --- | --- | --- |

**Cubic Equations**
Cubic graphs should have up to two turning points. They come in many forms. They do not have to be symmetrical. The equation for these graphs are in the form y = ax3 + bx2 + cx + d. This means the highest power would be x3. Below are some examples:

| y = x3 | y = -x3 | y = x3 - 8x |
| --- | --- | --- |

**Reciprocal Equations**
These graphs are all hyperbolas. This means they consist of two separate lines which are opposite each other as though they were a reflection of each other. The equations for this type of graph come in the form y = a/x. Below are some examples:

| y = 1/x | y = 10/x-2 |
| --- | --- |