∴ Let the analytical formula of parabola be,
Image pass (10,0),
∴ ,
Solve,
The analytical formula of ∴ parabola is; (2) When two vans with a width of 3m and a height of 3.5m run in parallel in the center, x=2,
Substitute x=2 into the analytical formula: y=-0.25(2-5) 2 +6.25, y=4,
∵4-3.5=0.5,
∴ The tunnel allows two vans with a width of 3 meters and a height of 3.5 meters to run side by side in the middle; (3) i suppose AO=x, we can get AB= 10-2x,
∴AD=-0.25(x-5) 2 +6.25
The circumference of a rectangular ABCD is l:
l = 2[-0.25(x-5)2+6.25]+2( 10-2x)=-0.5x 2+x+20 =-0.5(x- 1)2+20.5，
The maximum value of ∴l is 20.5,
Two. When the triangle with vertices p, n and q is an isosceles right triangle,
∫P on the image with y=x, let P(m, m),
A vertical line passing through point P as the X axis intersects the parabola at point Q,
∴∠ POA =∠ OPA = 45, and the coordinate of point N is (5,5).
The coordinate of point q is (m, 5),
Substitute in the coordinates of point Q, and you get,
Solve,
∴ Let a triangle with vertices P, N and Q be an isosceles right triangle, and the coordinates of point P are: (,) or (,).