Graphs form a big chunk of your GCSE Maths exam paper.

If you don’t know what the graphs look like i.e. what shape they are and where they cross the x and y axis, you will struggle and lose easy marks.

I highly recommend this tool: www.desmos.com

It’s an online tool that draws graphs for you, all you need to do is type in the equation.

The great thing about it is you get to see the graphs and play around with them. This makes it easier to remember and practice translations and transformations.

I used desmos to make the images in this blog post.

So what do you need to know?

Straight Line Graphs:

y = x

Things to note: crosses the origin

This is probably one of the first graphs you learnt, way before GCSE Maths.

It is literally a diagonal line that goes through (0,0).

x | -5 | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 | 5 |

y | -5 | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 | 5 |

Values for y = x

Things to know: How to translate the graph, how to work out gradients (we’ll cover this in another post), equations of straight line graphs: y = mx+c

Other Types of Graph:

Quadratic Graphs:

Things to note: Sits on the x axis at the origin, symmetrical in the y axis, highly likely to be asked to translate this graph.

This is a gorgeous graph, and you need to be able to sketch this and move it around if asked.

So when you’re playing with Desmos, add a +1, +2 etc. on the end and see how the graph moves.

Why is this graph always in the postive quadrants for y?

x | -5 | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 | 5 |

y | 25 | 16 | 9 | 4 | 1 | 0 | 1 | 4 | 9 | 16 | 25 |

Values for y = x^2

Cubic Graphs

Things to Know: It goes through the origin, highly likely to be asked to translate this graph.

Reciprocal Graphs: 1/x

And -1/x

Things to know: Reciprocal graphs can be used to show inverse proportion. They are undefined when x=0 and when y=0.

Those cool curves are called Asymptotes. Asymptotes are lines that get very close to the axis but never touch.

The line y = x and y = -x is the line of symmetry for these graphs… how cool is that?!

Exponential Graphs:

`\[y=a^x\]`

Things to know: a must be bigger than 0 for these graphs.

These graphs have a beautiful curved shaped that always lies above the x axis.

The y intercepet is at (0,1) because any number to the power of 0 is 1.

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