Lesson video

Hi, I'm Miss Davies.

In this lesson, we're going to be drawing the graphs of simple cubic functions, using a table of values.

What do you think a cubic function is? A cubic function is a function of the form f of x is equal to axe cubed, add bx squared, add cx, add d, where the value of a does not equal zero.

The highest power in a cubic function is three.

We are going to complete the table of values for the graph y equals x cubed, add 2x.

The highest power of this equation is three, which means it is a cubic graph.

Let's start by drawing out the table of values.

Our values for x range from negative three to positive three.

Let's start with x is negative three.

We're going to substitute this value into our equation.

This gives us y equals negative three cubed, add two multiplied by negative three.

Negative three cubed is negative 27, and two multiplied by negative three is negative six.

We now need to calculate negative 27, subtract six.

This gives us negative 33.

This is our y value when x is equal to negative three.

Next, we're going to look at when x is negative two.

We'll follow the same process.

Negative two cubed is negative eight.

And two multiplied by negative two is negative four.

Negative eight, subtract four, is negative 12.

When x is equal to negative one, we have negative one cubed, add two, multiplied by negative one.

Negative one cubed is negative one.

And two multiplied by negative one is negative two.

Negative one, subtract two, gives us a y value of negative three.

When x is zero, we end up with a solution for y of zero.

When x is negative one, our calculation is one cubed, add two, multiplied by one.

One, add two, gives us a y value of three.

When x equals two, the calculation is two cubed, add two, multiplied by two.

Two cubed is eight, and two multiplied by two is four.

Our y value when x is equal to two is 12.

Finally, when x is equal to three, we substitute this value into our equation, giving us three cubed, add two, multiplied by three, is 27, add six, which gives us 33.

This is our completed table of values.

Now that we've drawn out the table of values, we're going to draw the graph.

This is our table of values that we've just created.

I've drawn out my graph.

Let me show you how I did it.

We're going to start off with the x value of negative three, and the y value of negative 33.

This gives us the coordinate negative three, negative 33, which is here on the graph.

Next, we're going to look at negative two, negative 12, which is here.

Then, negative one, negative three.

If we plot that on our set of axes, it's here.

Then zero, zero, or the origin.

One, three is next.

Followed by two, 12, and then finally three, 33.

Once you have plotted all of these points, you can join them together using a smooth curve, as I have done to create my graph.

Here are some questions for you to try.

Pause the video to complete your task, and resume once you're finished.

Here are the answers.

The graph of y equals x cubed should cross through the origin, which is the point zero, zero.

Here is a question for you to try.

Pause the video to complete your task, and resume once you're finished.

Here is the answer.

The graph of y is equal to x cubed should also pass through the origin.

Here are some questions for you to try.

Pause the video to complete your task, and resume once you're finished.

Here are the answers.

Both of the graphs not only pass through the origin, they also have the same absolute values.

This means that the value's the same if you multiply one of them by negative one.

Both of the graphs are also a reflection in the x axis.

Here are some questions for you to try.

Pause the video to complete your task, and resume once you're finished.

Here are the answers.

The curves are the same shape on each of the graphs.

They have different y intercepts.

Here are some questions for you to try.

Pause the video to complete your task, and resume once you're finished.

Here is the answer.

This graph crosses the x axis in three different places, one of which is the origin.

That's all for this lesson, thanks for watching.