Lesson video

Hi, I'm Mr. Bond.

And in this lesson, we're going to learn about the translation of graphs.

You might've used the word translations before, in relation to translating shapes.

Let's see how this relates to translating graphs.

First we'll consider the sketch of Y is equal to X squared.

To sketch this, we'll use a table of values.

Finding the corresponding Y values, gives us this.

We've simply squared each X value.

And when we plot the graph of this, we get this.

Fairly recognisable as a quadratic graph.

Now let's consider the sketch of Y is equal to X squared plus five.

We'll use a table of values, and we'll also use the same values of X that we used in the table above.

What's the difference between the Y values in the table above, and the Y values for Y is equal to X squared plus five.

Each one will simply be five greater than the values above.

So we'll have nine, six, five, six, and nine.

And if we plot these points, we'll get a sketch that looks something like this.

So what's the same and what's different, about each of these graphs? Well, for the same values of X, the Y values for Y is equal to X squared plus five, a five greater.

So, every single point on that graph has moved up by five.

What do you think Y is equal to X squared subtract three would look like? You could use some graphing software online to check.

Now let's look at another example.

Again, we're going to compare our new sketch to the sketch of Y is equal to X squared, which we've already looked at.

We're going to sketch the graph of Y is equal to brackets X plus five brackets squared.

Let's use this table of values.

You'll notice that I've used different values for X, compared to the table above.

And it will become clear why once you found the Y values.

The Y values should be this.

You'll notice that are the same as the Y values of both, but for different values of X.

What do you notice about the difference between the values of X? The difference is five.

When we plot these onto our coordinator axis, you'll get something like this.

So looking at the graphs, what's the same and what's different? Hopefully, you've noticed that the graphs are the same size and shape, but each of the points has moved five to the left.

What do you think the graph of Y is equal to brackets X subtract three brackets squared would look like? Again, you could use some online graphing software to check.

Hopefully, if you investigated the further examples that I gave in each case, you'll be able to generalise looking at these graphs.

From the sketches, what can be deduced about the values for A and B? Pause the video to have a think and use even the video when you've finished.

Hopefully, you've spotted that A will be a positive value, and B a negative value.

Here is a question for you to try.

Pause the video to have a go and resume the video when you've finished.

Here are the answers, you needed to sketch Y is equal to X squared plus two, and Y is equal to X plus two, all squared.

Hopefully, you spotted that, Y is equal to X squared plus two, is a translation two units, in the positive Y direction.

And Y is equal to X plus two, all squared is a translation of two units in the negative X direction.

You then have to label the coordinates of the turning points of each graph.

And you could have done this, by considering that the coordinate of the turning point for our original graph Y is equal to X squared, was the origin zero zero and then considering each translation intern.

Here is another question for you to try.

Pause the video to have a go and resume the video when you've finished.

Here are the answers.

You might've spotted that our original function looks like a cubic function.

So if you were struggling to realise what was happening here, you could have used a table of values for Y is equal to X cubed, then Y is equal to X cubed subtract five and Y is equal to X subtract five cubed.

And then compared each of the three different graphs.

You could have also use some online graphing software to help if you wanted to.

Again we needed to write down the new coordinates of point A for each graph.

Point A was zero, zero.

So therefore, for the graph in a part one of question A, this would have been zero, negative five, a translation of negative five in the Y direction.

And then for part two of question A, it would have been five zero, a translation of positive five units in the X direction.

That's all for this lesson.

Thanks for watching.