### Video Transcript

Which of the following graphs
represents π π₯ is equal to π₯ minus one all squared?

To help us to understand this
question better, Iβve drawn a little sketch. And this sketch shows that the
function π π₯ is equal to π₯ squared. So as you can see, with this
function, what we actually have is a U-shaped parabola, which is symmetrical and
actually touches the origin at zero. So thatβs the shape of the curve
weβd get if it was π₯ squared.

However, our function this time is
π₯ minus one squared. And to help us with this, what
weβre gonna have look at is a little couple of rules for translation, so when weβre
translating a graph. Our first translation rule is that
if we had π π₯ plus π, itβs equal to a shift of π units in the π¦-direction.

And what it is important to note
here is that the plus π is actually outside the parentheses. So itβs- sort of not in the
parentheses with the π₯. So we know this is in the
π¦-direction. Our second rule is that π π₯ plus
π is equal to a shift of negative π units in the π₯-direction.

And the two key points to notice
this time are firstly that the plus π is within this- side the parentheses and
secondly is a shift of negative π units in the π₯-direction. So itβs important to know that
whenever weβre dealing with π₯-direction translations, that first of all, like we
said, the π will be inside the parentheses. And second of all, it does the
opposite of what you think. So itβs actually gonna be a shift
of negative π.

Great! So now we know this. We can have a look at the function
that weβve got and pick which graph would be suitable. Well, looking back at our original
function, we can say okay well therefore our function of π₯ minus one in the
parentheses all squared is gonna link to our second rule.

So therefore, this means that weβre
gonna get a shift of plus one unit in the π₯-direction. But what does this mean in actual
practice? So what does this mean to our
graph? Cause we look on the top right-hand
side, we can see our π₯ squared graph. Whatβs gonna happen to this?

Well, in practice, that actually
means that all our π₯-coordinates are gonna be increased by one. And the reason that itβs increased
by one and add one, cause remember if we look at the function, our π-value is
negative one. And remembering the rule, it says a
shift of negative π. So negative negative one gives us
plus one, or π₯-coordinates have all increased by one.

So Iβve sketched what happens on
our original graph. So if you have a look there, we can
see that actually our π₯-coordinates have all increased by one. So itβs been a shift to the
right. So now which one of our graphs will
that apply to?

Well we can see that itβs graph π
because that actually has the point where it touches the π₯-axis is actually at one
because it shifted one to the right. So therefore, we can say that graph
π represents π π₯ is equal to π₯ minus one all squared.