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It is known that the parabola y = x & # 178; + (2n-1) x + n & # 178; - 1 (n is a constant term) It is known that the parabola y = x & # 178; + (2n-1) x + n & # 178; - 1 (n is a constant term) (1) when the parabola passes through the origin and the vertex is in the fourth quadrant, the corresponding functional relationship is obtained. (2) Suppose that point a is a moving point on the parabola determined by (1), and it is located below the x-axis and on the left side of the symmetric state, passing through point a as a parallel line of the x-axis, intersecting the parabola with another point D, making ab ⊥ x-axis and point B, DC ⊥ X-axis at point C, then (1) when BC = 1, find the perimeter of rectangular ABCD (2) whether there is a maximum perimeter of rectangular ABCD? If it exists, calculate the maximum value and the coordinate of point A. if it does not exist, please explain the reason,
（1）n^2-1=0
n^2-1
N = 1 or n = - 1
When the vertex is in the fourth quadrant
So n = - 1
y=x²-3x
(2) The symmetry axis of y = x & # 178; - 3x is x = 3 / 2
When BC = 1
Then ad = 1
The coordinate of a is (1, ya)
The coordinate of D is (2, YD)
ya=1^2-3*1=-2
yd=2^2-3*2=-2
The coordinates of a are (1, - 2)
The coordinates of D are (2, - 2)
Perimeter = (2 + 1) * 2
=6
(2) Let the coordinates of a be (x, X & # 178; - 3x) with larger perimeter
Perimeter L = 2 * [2 * (3 / 2-x) - X & # 178; + 3x] has maximum solution
L=2*[3-2x -x²+3x ]
=2*[3-x²+x ]
=-2(x²-x -3)
=-2(x-0.5)²+6.5
The coordinates of a are (0.5, - 1.25)
The maximum solution is 6.5
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