Give the rule for y against x^2 which is marked at the point 2,6?

y = k x²

k = 6 / 4 = 3 / 2

y = (3/2) x²

There are infinite rules that fit the requirement. For example,

y = x² + 2
y = 2x² - 2
y = 3x² - 6
y = nx² - 4n + 6

y = (3/2)x²

y = -x² + 10
y = -2x² + 14
y = -3x² + 18
y = -nx² + 4n + 6

y = (1/2)x² + 4

………………. (and so on)

y = x^2+2

I do not think much of the sentence construction of that question, but it seems to say that y varies with the square of x. No partial variation is implied.

That would make this correct: y = 3x²/2

It would make this incorrect: y = x² + 2

Don't take that to the bank. It is only my interpretation. The question is not clear.

If this is exactly the whole question you were asked, your teacher is a moron.

Sorry, can you restate that? The question makes no sense.

If y = x^2 + 2 is correct, is y = 3x^2/2 also correct?