[Music] hello and welcome to our lesson on plotting Cuba crafts they were going to plot the equation why is it good to ask lead until unison we need to remember and I quote an iPad is made up of an x and the y value so we will begin with X equal 0 so this will be y is equal to 0 cubed so when X is equal to 0 Y will also be equal to 0 and we can plot this point at the origin the next one X is now 1 so our x coordinate is 1 and Y is equal to X cubed so why it's also 1 so when X is 1 Y is 1 and we can plot this point here I mean that one we know what I'd tell you if now in our Y value is y is equal to 2 cubed which is 8 so when X is 2 y is equal to 8 and this point goes here and when X is equal to negative 1 we have negative 1 cubed so we have negative 1 and negative 1 and this point will go here when y is equal to X which is negative T cubed Y will equal negative 8 shower coordinate if x equals negative 2 and y equals negative 8 so this partner would go here so to plot this graph we're going to join these points together with a smooth curve and now we can use this graph to solve the equation 5 to X cubed so we have the equation y equals x cubed and we're using this to solve five equals x cubed so we can see that y must equal 5 so we need to draw the horizontal line y equals 5 and where the two lines cross will be our solution to the equation 5 equals x cubed will draw a vertical line from the intersection to the x-axis and you can see the solution to X is approximately 1.75 so X is approximately 1.75 okay let's move on to my next question so you want to try this question yourself by plotting the graph of y is equal to H cubed minus 5 on the exact things by pausing a video and then you can resume it when you're ready ok so we have y is equal to X cubed minus 5 and I'm going to begin by plotting when x equals 0 so y is equal to 0 cubed minus 5 y will equal minus 5 so our coordinates are 0 and minus 5 which are here and then we have Y is equal to 1 cubed minus 5 y is equal to 1 minus 5 y is equal to minus 4 which is here the next we have y is equal to 10 cubed minus 5 y is equal to 8 minus 5 y is equal to 3 from this point we'll go here when x equals negative T so Y is equal to negative T cubed minus 5 y is equal to negative 8 minus 5 y is equal to negative 13 which goes here and finally y is equal to negative 1 cubed minus 5 y is equal to negative 1 minus 5 y is equal to negative 6 which goes here so now we can plot these points together with a smooth curve okay so we have plotted the graph and now we can use this graph y equal to X cubed minus 5 to solve the equation 3 is equal to X cubed minus 5 so you can see number y must be equal to 3 so I'll draw a horizontal line y equals 3 so head for line y is equal to 3 and you can see the two graphs do intersect I'm a point that when the intersect is where near equal to each other I'm by drawing a vertical line down you can see X is equal to 2 so X is equal to 2 when y is equal to 3 thank you very much for watching I hope you found that useful thanks again and take