Video Explanation

Text Explanation

To determine the value of k, it's going to be helpful to express the points A, B, and C in terms of coordinates. If the coordinates can be expressed in terms of k, then we can figure out the base and height of the triangle in terms of k. Then we'll be able to relate the triangle's area to the value of k.

Since A exists on the y-axis, its coordinates must be of the form (0, something). Thus, we can plug 0 in for x in the given equation for the parabola:

Therefore, the coordinates of A are (0, k).

Since B and C exist on the x-axis, their coordinates must be of the form (something, 0). Thus, we can plug 0 in for y in the given equation of the parabola:

Therefore, the coordinates of B and C are and , respectively. This allows us to update the diagram as follows:

Since we travel k units in the y direction, the height of this triangle is k. Likewise, since we travel units to the right and to the left along the x-axis, the base of the triangle is the sum of those two distances: .

We can now use the formula for the area of a triangle to determine the value of k:

That decimal is already rounded to the nearest hundredth, so we don't need to do any further rounding to satisfy the conditions of the problem, making 0.25 the final answer.

(Note: There are different conventions for rounding. However, for the purposes of the GRE, we round in the following manner: if the digit to the right is 0 through 4, we round down; if the digit to the right is 5 through 9, we round up. In this problem, since there is nothing (or "zero") to the right of 0.25, we would round down to 0.25.)