Graphs

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