Today’s SAT question of the day is a math question that is rated hard. If you work along with me step by step, I think you’ll see that this problem really isn’t so hard after all. In fact, we are even going to discuss two ways to solve it.

Here is the problem: we have a revenue model that is expressed by r(p) = 2,000p – 10p^2. We need to know which of the values in the answer choices will give us the greatest revenue.

Option 1: plug in the answer choices and see which one gives the biggest output.

Option 2: parabola time! This is, in fact a parabola. We could think of it as y = -10x^2 + 2000p.

This is a “frowny” parabola because the coefficient of x is negative. So, its maximum value will be at its turning point or vertex.

The turning point is on the axis of symmetry. We find the axis of symmetry with this: -b/2a. In our parabola, b is 2000 and a is -10, and -2000/-20 = 100. Are we done?.

Yes! This gives us the x coordinate of the turning point, which is the input for the function (or p in this case).

Either method will get you to the right answer – the second one might save you a minute or three, but neither one is especially hard…right?