There are some other types of graph that you should be familiar with:

**Quadratic Graphs and Quadratic Equations**

You may be asked to use a graph to solve a quadratic. For example solve the equation 0 = x2 + 2x – 3 using the graph y = x2 + 2x – 3 (shown above).

This is easy! Just look to see where y = 0 on the graph i.e. where the graph crosses the x axis.

So here you can see the answers are -3 and 1:

**X Cubed Graphs**

These have a kink in them. How big the kink is depends on the other terms in the equation.

So here is y = x^{3}

and here is y = x^{3 }+^{ }2x^{2 }+ 1:

and here is y = –x^{3 }+^{ }2x^{2 }+ 1 (notice it slants downwards from left to right):

So if asked to draw a cubed graph just plot enough points and join them by a smooth curve.**Exponential Graphs**

The graphs are in the form y = kx

If k is greater than 1 then the graph slopes up from left to right.

If k is less than 1 or is negative the graph slopes down from left to right.

They always go through the point (0,1) and are always above the x axis.

So here is the graph for y = 2x:and this is what it would look like if 2 was to the power MINUS x (see the surds page to realise this is actually 2 to the power a half):**Reciprocal Graphs**

These graphs occur when you have the basic formula y = A/x

This could be written xy = A

They only ever exist in two quadrants and they don’t touch.

Which quadrants they are in depends if they are positive or negative.

The graph for y = 1/x looks like this:and y = -1/x looks like:

**Circles**

The equation for a circle with centre (0,0) and radius r is:

**x2 + y2 = r2**

So x2 + y2 = 9 is a circle with centre (0,0) and a radius of 3:

**Sine And Cos Waves**

These waves wiggle up and down between one and minus one on the y axis. They repeat every 360 degrees.

Between 0 and 360 degrees the sine wave forms a nice wave. The cos wave forms a bucket between these values. Below you can see the sine wave in red and the cos wave in blue: