Lesson video

Hello, my name is Mr Clasper.

Today we are going to be plotting simple quadratic equations.

A quadratic equation is one where the highest power of x is two.

Here are some examples of quadratic graphs on the right-hand side.

What's the same about these equations? And what is different? If we look at these two graphs, we can see that both of them have x squared.

However, the second one also has a constant of negative seven.

These are still quadratic equations.

If we look at the second equation, we have three x.

However, the highest power is still two as we have x squared being the highest power.

For equation four, we have a coefficient of three for x squared, but again, this doesn't affect the fact that x squared has the highest power of two.

And for the last example, if we expand these brackets, we will have, y is equal to x squared, minus two x minus 35.

And again, this would have a highest power of two for x.

Let's look at the equation y is equal to x squared.

We're going to need to find some values for y, so let's use a table of values.

We're going to substitute each value of x into the equation to find a value for y.

First substitute x is equal to three.

I would get three squared, which is equal to nine.

When I substitute two, I get a value of four.

When I substitute one, I get a value of one.

And when I substitute zero, I get value of zero.

If I substitute negative one, this would mean, I need to calculate negative one squared or negative one multiply by negative one.

This will give me positive one.

Negative two squared will give me positive four and negative three squared will give me positive nine.

We now have a complete table of values.

Let's plot this information on a graph.

Here's our table of values from before.

Each value for x relates to an x coordinate and each value for y relates to a y coordinate.

So for example, on our graph, when x is equal to three, y must be equal to nine.

Therefore we can plot three, nine.

When x is equal to two, y is equal to four.

So we can plot the coordinate two, four.

And we can plot the coordinates one-one, zero-zero, negative one- one, negative two-four, and negative three-nine.

Once we've done this, we join our points with a smooth curve.

Here are some questions for you to try.

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

And here are your solutions.

So question one, make sure you don't make the same mistake as Denny.

So you need to make sure that when you square negative values, you have a positive answer.

A good way to tackle this, if you're using a calculator, put negative values into a bracket first, and this will solve your problem.

And for question two, the correct answer was the graph on the left.

So this is a quadratic curve with a line of symmetry.

Here's another question for you to try.

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

And here's your solution.

So again, just be careful with your negative values.

So if you put these into a bracket before inputting in your calculator, you shouldn't have a problem.

And when you plot your coordinates, you should end up with a smooth curve.

And here's question four.

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

And here are your solutions.

So your three graphs should look very similar, but in different points on the axes.

And if you look carefully, y equals x squared plus one, crosses the y axis at a value of y equals one.

And x squared plus two crosses at two.

And x squared minus one crosses at minus one.

So that constant is very important.

And here is your last question.

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

And here are your solutions.

So remember you need to make sure that you check your coordinates.

You should have a smooth curve and a line of symmetry.

So if one of your points or one or more of your points seems out of line, it might be worth checking your substitution again.

And Ella's graph was wrong because she's joined it with straight lines.

So her points are correct, but she's joined each one up with a straight line segment and you need to have a smooth curve.

And that's the end of our lesson of plotting simple quadratic equations.

Why not try the exit quiz to show off your skills? I'll hopefully see you soon.