What does g(x) look like as a graph? It's a good idea to draw a picture to help you visualise the answer to this question. When we show g(x) as a graph it looks like an inverted U with it's maximum point at (0,0). The graph never moves any further into the positive region of the vertical axis, that is, g(x), but it spreads itself symmetrically because the square of a negative number is the same as the square of the equivalent positive number (for example, -1 and +1 have the same square =1). This makes the vertical axis look like a mirror. Now to the question. The spread of the arms of the U is governed by the constant -3. The answer to the question must preserve the spread so we can reject option a, because that would be a narrower shape than g(x). Next we have to see which option puts the maximum point at f(x)=4. The maximum for g(x) is at (0,0) the "top" of the upturned U. We need to slide the U upwards, more positive, so we can reject option c, because it would force the curve downwards, more negative. We're left with options b and d. When f(x)=4 we know we must have x=-2 to satisfy the requirements, so we substitute this value into options b and d and for b we get a number which is far too negative, while option d gives us 4, so d is the right answer!