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In the figure below, the curve is a graph of the function y=ax2 (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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AB = 3-(-3) = 6
CD must also = 6 such that C is at (6,8)
Now let's figure out a in y=ax^2
by using the point C(6,8) which will help us to find y...

Being that C: y=a(6^2)
y=a36
8=a36
a=8/36 or a=2/9
So using point B(3,y) y=(2/9)*(3^2)
y=(2/9)*9
y=2
So, knowing that B is at (3,2) and D is at (0,8)
we know that h=8-0 or 8
So...since the Area of ABCD=base*height
Height=8
Base=6
Area=6*8 or 48 square units
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