ExpertMedium1 markMultiple Choice
AQA GCSE · Question 15.3 · Algebra
For the equation y = 3x², what happens to the value of y when x is doubled?
For the equation y = 3x², what happens to the value of y when x is doubled?
Answer options:
A.
The value of y is doubled
B.
The value of y is divided by 4
C.
It is not possible to say what happens to the value of y
D.
The value of y is multiplied by 4
E.
The value of y is halved
How to approach this question
1. Take the original equation, y = 3x².
2. Replace x with (2x) to represent doubling x.
3. The new equation becomes y_new = 3(2x)².
4. Be careful with the order of operations (BIDMAS/PEMDAS). Square the term in the brackets first: (2x)² = 4x².
5. The new equation is y_new = 3(4x²) = 12x².
6. Compare the new value of y (12x²) with the original value of y (3x²).
7. Describe the change.
Full Answer
D.The value of y is multiplied by 4✓ Correct
We are testing the effect of doubling x on the equation y = 3x².
Let's pick a starting value for x, for example, x = 10.
The original y would be y = 3 * (10)² = 3 * 100 = 300.
Now, let's double x. The new x is 2 * 10 = 20.
The new y will be y = 3 * (20)² = 3 * 400 = 1200.
Comparing the new y (1200) to the original y (300), we see that 1200 = 4 * 300. The value of y has been multiplied by 4.
Algebraically:
Original: y = 3x²
New x: x_new = 2x
New y: y_new = 3(x_new)² = 3(2x)² = 3(4x²) = 12x².
Since the original y was 3x², the new y (12x²) is 4 * (3x²), which is 4 times the original y.
Common mistakes
✗ A common mistake is to only square the x, not the 2. For example, writing 3(2x)² as 3 * 2 * x² = 6x², which would lead to the incorrect conclusion that y is doubled.
✗ Confusing y ∝ x² with y ∝ x.
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