Lesson video

Hi, I'm Miss Davies, in this lesson, we're going to be sketching graphs of cubic functions that are given as three linear expressions.

A cubic function is given by the equation Y is equal to X add five, multiplied by X add one, multiplied by X subtract two.

We're going to work out the value of Y, when X is equal to zero.

This means we're going to substitute X equals zero, into our equation, this gives us Y equals zero add five, multiplied by zero add one, multiplied by zero subtract two.

This simplifies to five multiplied by one, multiplied by negative two, giving a solution of negative 10.

The graph of Y equals X add five multiplied by X add one, multiplied by X subtract two, intercepts the Y axis at the coordinates zero, negative 10.

As we have just worked out that when the X value is zero, the Y value is negative 10.

Still using the same cubic function as previously, we are going to work out the values of X, for which Y is equal to zero.

When Y is zero, this means that either X add five is equal to zero, in which X would be equal to negative five.

Or X add one is equal to zero, in which X would be equal to negative one, or X subtract two would be equal to zero, giving the solution of X is equal to two.

We're going to write down the coordinates of the three points where the graph intercepts the X axis.

We already know that our Y value is zero and we've worked out our three possible values for X.

This means that the three points where the graph intercepts the X axis are, negative five, zero, negative one, zero and two, zero.

We are now going to sketch this graph using the information that we have just worked out.

We know that the Y intercept is zero, negative 10.

We also know that the X intercepts are negative five, zero, negative one, zero and two, zero.

Our cubic graph looks like this.

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 curve of your graph might look slightly different to this one.

As long as the general shape is similar, that's fine.

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, this graph has a positive Y intercept, because it has two positive X 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 touches the X axis at negative three, but it doesn't go through that point.

With this next example, we have been given a sketch of the graph and have been asked to work out the function that is shown by this graph.

We can see from the graph, that the X intercepts are negative eight, zero, negative two, zero and three, zero.

From the previous examples, we know that this means that when Y is equal to zero, X is equal to negative eight or negative two or three.

This gives us the function or the equation, Y is equal to X add eight, multiplied by X add two, Multiplied by X subtract three.

We can check that this is correct.

If we multiply together the three bracket, when X is equal to zero, this should give us the value of negative 48, and this is the Y intercept of the graph.

Eight multiplied by two, multiplied by negative three, is negative 48, so this is our function.

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 on part B only touches the X axis at the point one, zero.

This means that the bracket X subtract one, appears twice in the function, or it is squared.

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