A quadratic function is just an expression (collection of letters and numbers) where the highest power of any unknown is 2.

What makes it a function, rather than just an expression, is that it will usually say ‘y = ‘. This is important, as without that part it’s not something we can plot on a graph!

e.g. y = x2 + 5

[It doesn’t have to be ‘y = ‘ by the way, it could be any letter, but in Pure maths, we typically just stick with ‘y = ‘ to keep things simple. In the real world, professionals will change that to whatever they need, depending on their work and their situation (e.g. instead of just ‘y = ‘ they might use ‘P = ‘, where P stands for profit, or ‘C = ‘, where C stands for cost.) ]

It’s possible to plot these easily using a table of values, the same way you can plot a linear graph. The more points you take, the more accurate your curve will be.

There are two important differences:

The points must be joined by a smooth curve, not straight lines! GCSE exams will often try to trick you, by giving you two points near the top or bottom which have the same y value. When plotting graphs many candidates make the mistake of joining these together with a straight line, giving their graph a flat bottom or top. The top/bottom must always be round! So your graph will need to dip just below, or just above, these two points.

It's important to recognise what a basic y=x2 looks like.

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