# Video: Pack 2 • Paper 1 • Question 7

Pack 2 • Paper 1 • Question 7

02:46

### 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.