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.
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:
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:
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:
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: