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Yes im answering a japanese test problem. its a long ass story and i dont feel like explaining bc i dont feel like breaking down about it now. i just want to end it (or it ending me). I also dont know if i chose the right tag because the test im taking is a mix of so many things.

So anyway a rough translation of the problem is :

In the figure on the right, the curve is a graph of the function y=ax^2 (a > 0), and two points A and B with x-coordinates of -3 and 3 are placed on the curve. Also, take a point C on the curve whose x-coordinate is greater than 3, and let D be a point on the axis with the same coordinate as C.

When the y-coordinate of the point D is 8, the quadrilateral ABCD becomes a parallelogram. At this time, the value of α and the original

Find the area of the parallelogram ABCD.
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Area of parallelogram is base times heights. You already have length base AB ( =6)

Since ABCD is a parallelogram, that means AB is parallel to CD and both have same length. This means, you now have coordinates of point C=(6,8). You only need y to calculate the height.

Both points B and C are on the graph of function y=ax^(2) . Plugging their coordinates in the function's formula you get two equations:



From the second equation you can calculate a=2/9, and plugging that in the first equation you get y=2

Now you can calculate height and area.

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