 I'm Lucy and in this video we're going to look at how to plot cubic graphs. Cubic functions are actually really useful. They are found in digital cryptography, so keeping things safe online. They come up when investigating a drag on aeroplanes, or studying the wind and wind turbines, and even in animations on computers. So there is some motivation for learning what they look like and how to plot them. If you've already watched our videos on plotting straight lines and plotting quadratics, then you'll already know all about table of values. And for cubics, it's the exact same process. Straight line equations look like this on the graph, and quadratics either look like this or like this. So cubic functions, they will look like this or like this. So when you see that x cubed is the highest power, you know that it's going to be a cubic function. And if it's a positive x cubed, it will look like this. And if it's a negative x cubed, it will look like this. So let's look at an example. We want to plot y equals x cubed minus 5x on our graph. It is a positive x cubed, so we know we're expecting something like this. So we start with our table of values, and we will need at least five sets of coordinates for cubics. I always start with zero, so let's substitute that into the equation. y equals zero cubed minus 5 multiplied by zero. So y equals zero minus zero, which means y is zero. So when x is zero, y is zero. Enter these coordinates into the table. Your turn now. Pause the video and work out the y coordinates when x is one, two, and three. Click play when you're ready to check. Did you get negative four, negative two, and twelve? Let's have a look at what these four coordinates look like on our graph. The three twelve doesn't fit onto our graph, so we'll just ignore it. So we have half our cubic, but as we know what shape we're expecting, we'll have to substitute in some negative x values to find the other half of the curve. So x is negative one, x is negative two, and x is negative three. Substitute these three values into the equation. Pause the video, work out the y coordinates, and click play when you're ready to check. Did you get four, two, and negative twelve? Let's now plot these three coordinates onto our graph and see what shape we get. Again, the negative three twelve is off our grid, but it helps us to see the shape. Join up the points of the smooth curve. Do not use a ruler and continue the curve on past your points so it covers the whole graph. Make sure you do it in pencil so that you can erase it and try again if you need to. And the final piece of the puzzle, label the curve with the equation. Luckily for you, you're usually given the x values in the table of values, so you know what to substitute in. So you should now know how to plot cubic graphs using a table of values. It's the x cubed that tells us it's going to be one of these shapes, and we need a minimum of five sets of coordinates to make sure we get the right curve. Luckily for you, you're usually given the x values that you need to substitute in. And if you want a really quick way of finding that table of values, watch our Plotting Graphs Calculator Trick video to see how. Bye!