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Find an equation of a parabola that has curvature 4 at the origin.

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The way to attack such a problem is to read it carefully and gather all the data given in it. In this case, it is not hard, but in some cases you have to read very carefully, to avoid missing some fine point which gives a required clue. Here it says, "Find the equation of a parabola..." - so we know that the curve is a parabola, and immediately we should think of the equation of a parabola:

y^2 = 4ax [where ^ stands for "raised to the power"]

Where a is a constant whose value we do not know ...

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