YOU ARE LEARNING:
Cubic Graphs
Cubic Graphs
Cubic graphs are curved graphs, where the highest power of x is 3. A table of values can be used to work out each point on the graph.
Cubic graphs are functions where the highest power of x is x3. They can have a variety of shapes depending on the specific function being displayed.
Let's draw the graph of y=x3−2x2−5x
For each x coordinate, we can find the corresponding y coordinate by ....
.... substituting the x value into the equation.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/NLV8SJyXSVuoKbrlR3W8.png)
For example, when x=1, y=−6
y=13−(2×12)−(5×1) so y=−6. We can plot this point on the graph at (1,−6)
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/hhVObsGAReqapJI4avgm.png)
What is y when x=−2?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/hhVObsGAReqapJI4avgm.png)
When x=−2, y=−6
This is because y=−23−2(−22)−5(−2). Remember that a negative multiplied by a negative equals a positive. We can plot this point at (−2,−6)
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/hlmZTBBUSpyyaJ1dUilz.png)
What is y when x=2?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/hlmZTBBUSpyyaJ1dUilz.png)
When x=2, y=−10 y=23−(2×22)−(5×2)=−10.
We can plot this point at (2,−10). Let's try filling out a few more values in a table.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/Dsgm9nRoTzKSG1IU1Qil.png)
The graph of y=x3−2x2−5x
We can use a table of values to help find points which will allow us to draw a cubic graph.
In this table we can see the points we have already calculated for when x=−2,1,2 .
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/nCTOyKjCRdyT0j1xsewf.png)
Let's fill this table out so we have more points to help us find the curve. What is the y-coordinate for when x=−1 ?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/nCTOyKjCRdyT0j1xsewf.png)
What is the y-coordinate for the point when x=3 ?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/xq6EiMYCSC6byYr2vYXb.png)
What will be the point when x=4 ? Give your answer in the form (x,y) .
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/vxrHzGXQ0yW7qJvHp5gg.png)
Nice!
Now we have enough points to draw a line.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/QHAwhcu4TaGokhdAzFnA.png)
the graph of y=x3−2x2−5x
Here we can see all the points we calculated plotted on the graph.
Now all we need to do is join these points up with a smooth curve.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/k6RXvmlxQMG9BqYEOvuQ.png)
Awesome!
This is the line of y=x3−2x2−5x.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/eQZQTlJjShypxWhUT7sn.png)
Let's draw the curve of y=x3+x
Remember, we can find values of y by substituting values of x into the equation.
Let's give it a go
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/NLV8SJyXSVuoKbrlR3W8.png)
What is y when x=1?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/NLV8SJyXSVuoKbrlR3W8.png)
What is y when x=−1 ?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/4s94uvaRCOGG08ZGhOkR.png)
Does the curve pass through the origin, (0,0) ?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/EOOfQphITDuZiinthooX.png)
What is y when x=−2?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/HPg4gXQrR4GwzcAKdOSS.png)
Awesome! We have enough points
Now we can draw a line to smooth join the points together.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/1hlW6EMyS0CRsHDzNLnk.png)
This is the line of y=x3+x
Nice!
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/N7WAg71S6iy7bCPsBNH8.png)