Ok. They tell us the equation of that parabola is
y =
ax2. Whenever you get a question like this (which is not all that uncommon in the hard math questions) you're looking to
find a point on the graph! Since they also tell us that the area of the square is 64, we know the sides of the square must each be 8:
Since parabolas are symmetrical and this one has its minimum at (0,0), we know now what the actual points are at each corner of our square:
And that, friends, is where this gets fun. Let's use (4,8) since both numbers are positive. Now that we have a point on our parabola, we just need to plug values in for
x and
y!
y = ax2
8 = a(4)2
8 = 16a
0.5 = a
This would, of course, also work with (-4,8).
Either way, you're going to get 0.5 (or 1/2) for a.
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