Lesson video

Hello my name is Mister Clasper and today we are going to be plotting other quadratic equations.

Let's have a recap, in a lesson on plotting quadratic equations we looked at these five equations to identify what a quadratic equation looks like.

How do the equations circled differ to the ones from this lesson? Well, if we look at each, the first equation involves X squared, three X and five, the second equation involves three X squared.

So in this example, we have a coefficient greater than one, four X squared and our last example is written in a different form.

So we can still have an equation in this form, however, when we expand these brackets we would end up with X squared minus two X minus 35.

Let's look at this equation Y is equal to X squared, plus two X minus three.

This means to find the value of Y we need to take the value of X and square it, then add two lots of this value of X and then subtract three.

This is what my table of values could look like.

So the first thing we can do is take all of our values of X and find the value of X squared.

We then need to add two X, so if we take all of our original values of X and multiply these by two, this will give me each value for two X.

And I also need to subtract three, notice that this value doesn't change as this is our constant.

Our last step is to find out value for Y, so we know for example, when X is equal to three, X squared has a value of nine, two X has a value of six, and we need to subtract three.

So we can calculate nine plus six minus three, which would give us 12.

When X is two, we can calculate four plus four, minus three, which would give us five.

In the next column, one plus two, plus minus three or one plus two, minus three would give a zero.

When X is zero, we get a value of negative three.

When X is negative one, we have a value of negative four.

When X is negative two, we have a value of negative three.

When X is negative three, we have a value of zero.

Notice that there is some symmetry between where X is equal to negative three and where X is equal to one.

Let's plot the graph.

This is our table of values, when X is equal to three, we have a value of 12 for Y.

So we're going to plot the coordinate three, 12.

We can plot the coordinate two, five as when X is equal to two, Y is equal to five.

When X is equal to one, Y is equal to zero, so we can plot one zero, and we can continue doing this.

Once all of the points are in, we then join this up with a smooth curve.

Notice that there is a line of symmetry at the point where X is equal to negative one, which mirrors the pattern that we found in terms of symmetry from the previous example.

Here's a question for you to try, pause the video to complete your task and click resume, once you're finished.

And here we are solutions, make sure you take care substituting X values, particularly when these are negative and you wish to square them.

So negative values, if you put them into a bracket and then square them on your calculator, they should solve any issues.

And if you check your graph, you should have a smooth curve, which crosses the point where Y is equal to negative four.

Here's another question for you to try, pause the video to complete your task and click resume once you're finished.

And here we are, solutions.

So for this question, it's very important that you square your value for X first, before you multiply by two.

And once again, when you square a negative value, if you're using a calculator, put your negative value into a bracket first, and it will solve any issues that you may have, so for example, negative three squared should be nine and then you can multiply this by two, which should give you your Y value of 18.

And here is your last question.

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

And here we are solutions, so similar to the last question, just be careful when you're substituting.

So you need to make sure that you square your values for X first, before you multiply each by three.

And if we move ahead to part C, the question is, does the point four, 48 lie on the graph? Well, we have an X value of four and a Y value 48, so they should mean if it is on the graph, we can substitute X as equal to four, and we should get a value of 48 And as we do, this means that this coordinate does lie on the graph.

And that brings us to the end of our lesson.

So you can plot a whole range of quadratic equations now, why not try our exit quiz to show off your skills? I'll hopefully see you soon.