Video: AQA GCSE Mathematics Higher Tier Pack 3 • Paper 3 • Question 13

Which of these points lies on the curve 𝑦 = 4𝑥²? Circle your answer. [A] (1/2, −1) [B] (2, 16) [C] (1, 16) [D] (−3, −36)

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Video Transcript

Which of these points lies on the curve 𝑦 equals four 𝑥 squared? Circle your answer. The possibilities are a half, negative one; two, 16; one, 16; or negative three, negative 36.

To answer this question, we could just substitute each possible 𝑥-value into the equation of the curve and work out the corresponding 𝑦-value to see which pairs of coordinates do satisfy the correct equation.

We do need to be a little bit careful with the equation of this curve though. And we need to remember the order of operations BIDMAS which tells us that indices or powers come before multiplication. This means that if we’re calculating four 𝑥 squared, we have to square 𝑥 first and then multiply the result by four. A common mistake would be to multiply 𝑥 by four first and then square our answer.

We can see that these two processes will give different answers if we consider what happens when 𝑥 is equal to one. If we apply BIDMAS correctly, then we’re squaring one first and then multiplying by four. One squared is equal to one. So we have four multiplied by one which is equal to four.

If, however, we applied BIDMAS incorrectly, so we multiplied the one by four first and then squared it, we’d have four multiplied by one all squared which is equal to four squared which is equal to 16.

Notice that one, 16 is one of the possibilities we’ve been given but it’s a red herring because remember this was an incorrect application of BIDMAS. The correct value of 𝑦 when 𝑥 is one is four not 16. So we can eliminate this point. We can actually eliminate two other points without any calculation if we consider what the graph of 𝑦 equals four 𝑥 squared looks like. It’s a quadratic curve. And as it has a positive coefficient of 𝑥 squared, it’s a U-shaped curve.

When we square an 𝑥-value whether it’s positive or negative, we always get a positive answer or zero. And when we multiply this by four, we’ll still get a number that’s positive or zero which means that 𝑦 is always greater than or equal to zero.

So we can eliminate the coordinates a half, negative one and negative three, negative 36 because they each have negative 𝑦-coordinates. So there’s no way that they can lie on this curve. This only leaves the point two, 16. But let’s confirm that this does indeed lie on the curve by substitution.

We can substitute two into the equation of the curve for 𝑥 and we have four multiplied by two squared. Remember we must square two first. So we have four multiplied by four which is equal to 16. This is the correct 𝑦-value for the pair of coordinates we’ve been given.

So we can conclude that the only one of the four points which lies on the curve 𝑦 equals four 𝑥 squared is the point two, 16.

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