Lesson video

Hello, my name is Mrs. Buckmire.

and today, our lesson title is Plotting Quadratics two.

Now, in Plotting Quadratics one, I introduced everyone to plotting quadratics.

And in this lesson, we're just going to do a bit more practise of identifying quadratics and plotting quadratics.

Okay, so make sure you have something to write on and something to write with.

Please pause the video whenever I asked you to, but also whenever you need to, remember, you can rewind.

Sometimes, it's helpful to hear something a second or even third time.

Okay, so make sure you're ready for our lesson and then let's begin.

Okay, so before you try this, I want you to fill in the missing values in the tables.

Okay, pause, you can go to the worksheet and see this.

And then make sure you resume the video so we can go through it.

Okay, here you see the majority of the answers.

So you can pause and check if those are correct.

Okay, so when we're filling the table, what we're doing is we're substituting, aren't we? So here we substitute negative three into X squared we've got nine.

Okay, so here the missing one that I haven't yet filled in, so here the Y value is given.

So we know that 15 equals X squared take away two X.

And also you might predict, it looks like it's between one and nine.

Did you have a go by substituting those values in? Did you try something else? Okay, in the end what did you get? Good, so five works out here.

So five squared is 25, takeaway 10 is 15.

So well I don't know if you got that.

It's really important that you're confident with substituting values in.

So do go back and check if there's any that you're unsure of.

Okay, so my question to you is, what do you notice? Okay, so make sure you pause and have a thought about what you notice about this, these tables.

Well the values in the tables.

Okay, so what we notice, well you might have noticed, is that it seems like a lot of them are positive, aren't they? Except here actually.

Here there's one value negative.

Okay, and what you might have noticed is here it kind of gets smaller, gets smaller, gets smaller, gets bigger, gets bigger.

Get smaller, then gets bigger, then gets bigger, bigger, bigger, gets smaller, smaller, smaller, then bigger and bigger.

So it's not, it doesn't keep getting bigger or keep getting smaller.

Seems to be, like in some predicaments its getting smaller to a certain point, and then it's getting bigger to a certain point.

Interesting.

Okay, Binh an Xavier decide if this equation will produce a linear or quadratic graph.

Binh says it's not a quadratic, 'cause there's no X squared.

Xavier says, "I think it is a quadratic.

"One coordinate on the curve would be five, 10".

Hmm.

Who do you agree with? Pause the video and have a think.

Okay, what do we think, who do we agree with? Binh? Xavier? Hmm, let's see.

I agree with Xavier.

So, why? Maybe, you expand it.

So, if you expand this, what do you get? X so it means we multiply all the terms on the outside with all the terms of inside.

And we get X squared subtract three X.

There you go, there is X squared.

So the reason why there was no X squared, is 'cause actually it was in a factorised form.

So factorization is like where we just display the factors and X next subtract three are factors of X squared takeaway three X.

And so actually that's why you couldn't currently really see an X squared, but actually when we evaluate it, we can see there is an X squared.

So it is a quadratic.

And at one point on the curve would be five 10.

Was that correct? So let's put five in as X.

So five times five takeaway three.

So five times two it is ten.

The Y value does equal 10.

So yes, that was a point on the graph as well.

So this was a quadratic equation.

Well done, if you got that.

Okay, so for your independent tasks, I want you to decide if the following equations will produce quadratic graphs or not.

If it is quadratic, can you match the equation with one that would produce the same curve? And you can check this by testing with coordinates.

Again, so, pause the video.

You can look at the worksheet for this and or you can do it on the video, but make sure you resume the video afterward so we can go through it.

Okay, pause in three, two, one.

Okay, so here I have put in pink or shaded the ones which are not quadratics.

Okay, so they do not have X squared.

So quadratics have the highest degree of X is two and here.

Where's my part to look at? Here, this, the power of X, not sure if you'll know this, but if you do, tell me now.

Yes, it's X to power half.

So that the highest power X is not two.

And this one actually equals to that one.

So that one actually equals to that one as well.

And, and it's not correct.

This one, do you know the power of X is here? Good, it's to.

where the power of X is to a negative one.

So again, if our highest power is not, this one's not, and you'll see that each one actually is not a quadratic.

What is this one? What type of graph is this going to be? Excellent, it's going to be a linear.

And what about this one? Good, this one's linear as well.

Okay, let's see which one match.

There you go.

So, I'm going to go through a couple of them.

So this one is quadratic and matches to this one.

So if we divided this one both by two, both sides by two, we'd get Y over two equals X squared.

It actually also matches to this one.

So here, maybe from looking at the one up there, the blue one up there, that I've squared put a square round, a rectangle round even, if you do the roots of them X squared, you'd get to this as well.

Even better if you want to be exactly right you could put plus or minus.

But then it depends on the graphs.

That's no big deal.

We had this one.

Quadratic matches this quadratic.

So one is the expansion of, the other one is the factorised version.

And, this one matches this one.

And you can see again, this one is the factorised version of this one.

This is the expanded, so that's all quadratics.

Well done if you got those right.

And as we explore, I want you to decide if these are quadratic, linear or other graphs.

And then I want you to plot the graph to see if you're right.

So this is where you get to practise your plotting, make a table of values, and.

And then what my real question is, is do any of the quadratics have any coordinates in common? That's what you're looking out for when you're doing this.

Okay, so this might take you a bit of time to make their five tables and to do all the graphs, but do spend time on doing it as accurately as possible.

And when you're plotting try to plot it with X, 'cause that's normally more accurate.

Okay, pause the video in three, two, one.

Okay, if you hadn't got it or just got stuck, remember, that, like, you could just do it.

I'm giving you that you could do it between negative three and three.

So do negative three, negative two, negative one, zero, one, two, three.

And just substitute the values in for each Y in here.

Okay, and then it might be helpful to actually plot them all on the same axis.

So here I've got an axis, and it doesn't matter if you don't have like graph paper, you can kind of just do it approximately even.

But we have our Y-axis, our X-axis.

And if you plot like two or three on the same one, then that might help you see if any of them coordinates have any, if they have any coordinates in common.

Okay, so there just plot.

Do go and have a little go at it.

And, I think maybe it could help if you make Y the subject as well.

So maybe say Y equals.

So here I'm taking away X on both sides.

So it's 10 take away X, and this one equals.

Now what is 10 squared? What does that mean? Good, it means 10 times 10.

So that really is X plus Y equals 100.

And then I want to make Y the subjects.

So what am I going to do? So isolate Y by, subtracting X from both sides.

So, it's equivalent to Y equal 100, take away X.

And here, maybe you want to actually expand, it might help.

So I'll just write, expand.

Okay, so hopefully that's enough, it can take you how to go and have no idea and come back again.

And, let's see if you can have a l.

a bit more time on that, and then I'll go for your answers in a moment.

Pausing in three, two, one.

Okay, so I thought to show you using Desmos.

So Desmos is a free website.

If you google Desmos graphic calculator and it'll come up and that's where you can check while I'm checking as well.

So, Y equals X squared plus X.

That is a quadratic.

Th.

and the other quadratics, which one was exactly the same as this graph? Good, Y equals X brackets X plus one.

So, why were they the same? Good, this second one is the first one factorised or this first one is the second one expanded.

So they are exactly the same quad.

So, which coordinates are equal? All of them.

Every single coordinate.

'Cause they have the exact same graph.

Okay, any other quadratics? Excellent, so two X squared equals to Y.

Oh.

And it looks like they're in the sector zero, zero, and one, two.

So one's because they had those coordinates in common.

Okay, were there any other quadratics? Let's see, what was X plus Y equals 10 squared.

What do you think it's going to be? Here it is, it's a straight line.

It doesn't even appear right now, let's zoom out.

There it is.

It's a straight line.

The negative gradient goes for 100 here and 100 here.

So that might have been really difficult actually to draw on the same axis.

Let's see if there's any, ones in common.

So there are some intersections, but it's quite hard to see.

So it looks like they're decimals.

So there's here, a negative 11.

05 and 111.

05.

Negative 7.

325 and 107.

325 is one set of coordinate.

I'm guessing this might be actually 6.

825, 93.

175 and here.

So you see how you might not plot that.

Especially if you used mine and just did it between three and negative three, then actually you.

Are there actually anything between it? No, they were higher.

So actually maybe you wouldn't have spotted that.

So that's why graphic calculators are so useful.

And that's why graphs in general are just so useful.

When we model things, we can kind of, get to just find out lots of things.

Okay, and the last one, Y plus X equals 10.

Before I draw it, what type of graph is it? X and.

is a straight line.

Let's see what it looks like.

Y plus X equals 10.

Here.

Aah interesting, looks like it's parallel to the the line.

Let's see when they intersect.

So it doesn't intersect X plus Y equals 10 squared at all.

But it does intersect our other two by dots, but they're not all numbers in.

So it's here.

and here.

So if you've got those kind of close approximations, and Oh.

So here we have two eight.

So there is one integer coordinates and then negative 2.

5, 12.

5 and negative 4.

317, 14.

317.

So we weren't expecting to get these, but hopefully you've spotted a few points where they.

where they did intersect.

Maybe you like guessed decimals around these values.

Well done, if you had a go.

Okay, thank you so much for all your hard work today.

Hopefully you had a good practise at identifying quadratics.

So when do we know it's quadratic? Good, when the highest power of X is squared.

So it's when the X squared is the highest power.

But we kind of need to evaluate, we need to expand brackets, we need to find out actually what the highest power of X is.

And what do quadratics look like? Good, they're those curves that are kind of a smiley face or sad face depending on what it is.

And we can plot a table of value sometimes to help us see the shape and to plot the coordinates.

Okay, so write down anything extra that you think you've learned today.

Please do the exit quiz as well, because I think that'd be super helpful.

And I hope you've enjoyed the lesson and have a lovely day.

Bye.