[Music] in this video we're looking at quadratic graphs which are graphs like these three that represent quadratic equations and if you take a look at these three equations along the bottom the reason they're quadratic equations is because they all have an x squared term but importantly they don't have any higher powers of x like x to the 3 x to the four and so on the most important thing to know about quadratic graphs is that they always have this smooth curved shape and there's also always a line of symmetry in the middle where the left and right sides are perfectly symmetrical the other thing to know is that if the x squared term is positive like it is for these first two graphs then the curve will be facing upwards like a smiley face whereas if the x squared term is negative like it is in this last example then the curve will be upside down like an unnappy face so just remember that a positive x squared means a happy graph and a negative x squared means an unhappy graph now the simplest quadratic graph that you'll see is probably this one y equals x squared when you only have an x squared term and there aren't any x terms or number terms then the only place that your graph will cross the axis is at 0 0 the same goes for y equals minus x squared but this time it curves downwards instead because the x squared term is negative the more you change the equation though the more different the curve will look for example if instead of y equals x squared we had y equals 2x squared the curve would become a bit narrower like this while if we had 2x squared minus 3 then the curve would move down a bit and if we had 2x squared minus 5x minus 3 that would move even further down and over to the right you don't need to worry about how all of this works exactly and what changing each of these numbers would do but you just need to understand that changing the numbers in the equation will change the shape of the graph anyway that's it for this video it was only a quick one today so cheers for watching and we'll see you next time