### Video Transcript

A student drew this for the graph
of 𝑦 equals 𝑥 squared minus two. Identify one error that the student
made.

Well, the first thing we’re gonna
do to actually help solve this problem is work out some 𝑥 and 𝑦 values that should
be there in the graph of 𝑦 equals 𝑥 squared minus two. So for the first value, I’ve got 𝑥
is equal to negative one.

Well, what we’re gonna do is
actually substitute negative one for 𝑥 in our equation 𝑦 equals 𝑥 squared minus
two. If we do that, we’re gonna get 𝑦
is equal to negative one all squared minus two, which is gonna give us 𝑦 is equal
to one minus two. And that’s because if you have
negative one squared, it’s negative one multiplied by negative one, which gives us a
positive. So we’re gonna get 𝑦 is equal to
one minus two. So therefore, 𝑦 is equal to
negative one.

So now we actually move on to
calculate the next pair of coordinates. We’ve got 𝑥 is equal to zero. Well, now for this one, what we
actually do is we substitute 𝑥 is equal to zero into our equation. So we now have 𝑦 is equal to zero
squared minus two. Well, zero squared is just
zero. So therefore, we’re left with a
𝑦-coordinate of negative two.

So it’s great. We’ve got two points. I’m just gonna do one more cause
then we can compare them fully. It’s gonna be the point where 𝑥 is
equal to one. So therefore, when we do this,
we’re gonna get 𝑦 is equal to one squared because we substitute in 𝑥 for one. So we’re gonna have 𝑦 is equal to
one squared minus two. So therefore, 𝑦 is gonna be equal
to negative one because if we have one squared, we get one. And one minus two is negative
one.

Okay, great! So we’ve now found the three pairs
of coordinates. So therefore, if we actually mark
on our points, we’ve got one here at negative one, negative one; one at zero,
negative two; and one at one, negative one. So we’re gonna take a look at the
middle point. So we’ve got a point zero, negative
two. And what we want to do in this
question is actually work out one error the student has made. And we can actually see that the
corresponding point will be this point here.

So therefore, we can see that on
the drawing that should be, so if we were gonna draw the graph, the point should be
at zero, negative two. However, we can see that, on the
student drawing, it’s actually at negative two, zero. So therefore, we can say that one
error that the student has made is the fact that the 𝑥- and the 𝑦-coordinates have
actually been swapped.

And therefore just to double-check
this and make sure that it’s correct, what we can actually do is look at some of the
other points we’ve plotted. So we’ve got the point here at one,
negative one. Well, if we look at the
corresponding point on the student’s graph, we see one at negative one, one. And therefore, yes, that agrees
that an error that the student has made is that the 𝑥- and 𝑦-coordinates have been
swapped.