 So in this video, we're going to look at how to plot quadratic functions onto a graph. You should already know how to plot straight line graphs using a table of values, but if you've forgotten, watch these videos first. There is nothing new to learn for quadratics other than the shape we are expecting. Quadratic functions are either U-shaped like this or N-shaped like this. Now what is a quadratic exactly? How do we know that we are looking for the U or N-shape? Notice how both of these curves had an X squared as the highest power. This is what makes them a quadratic. The U-shaped had a positive X squared and the N-shape had a negative X squared. That's really easy to remember because N is for negative. Okay, so now onto plotting one. Let's give this quadratic a go. Y equals negative a half X squared plus six. So the negative a half X squared tells us it's going to be N-shaped. So just jump straight in with our table of values. I have already given you the X values to substitute in. Pause the video, work out the Y coordinates and click play when you're ready to check. Did you get these Y values? If you've got them right and want to skip the working, click here. Otherwise, keep watching. So let's run through the working for substituting in X equals negative four. So we get Y equals negative a half multiplied by negative four squared plus six which gives us negative a half multiplied by 16 plus six. So negative a half multiplied by 16 is negative eight. So then negative eight plus six means Y is negative two. So when X is negative four, Y is negative two. Just be careful with multiplying negatives. This is where people make their mistakes. So with our table of values, we can just go ahead and plot our graph. Join the points with a smooth curve. Use a pencil so that if you make a mistake, you can erase it and start again. And make sure you extend the graph across the whole grid. And as always, label the curve with the equation. So that is all there is to it. You use your table of values to get coordinates which you then plot until you either get the U or N shape that you're expecting. Just remember positive X-squares are U-shaped and negative S-squared are N-shaped. You will need at least five coordinates to plot a quadratic but maybe more until you are getting the symmetrical curve that you're expecting. Sometimes you may need to choose the X coordinates yourself. But a bit of trial and error and you will soon work out which ones will fit onto the graph. See how the negative 412 and 436 will not fit onto our graph. So let's try X is three and X is negative three instead. So now the negative 3-1 does fit onto our graph. But the 3-19 is still too big. So let's just try X is one instead. Perfect! All of these coordinates fit onto our graph and so we can plot it accurately. Watch our table of values calculator trick for a sneaky, easy way to complete the table of values without having to do the work yourself.