∴5=4? 2b+c? 3=c,
Solve b =? 2c=? 3.
(2) The analytical formula of parabola can be obtained from (1): y=x2-2x-3=(x- 1)2-4.
∴M( 1,-4),
When y=0, then x2-2x-3=0,
∴x 1=3,x2=- 1,
∴A(- 1,0),B(3,0),
∴AB=4,
∴S△ABM=4×42=8.
The coordinate of point P is (a, a2-2a-3). When the point p is above the x axis,
∴4(a2-2a-3)× 12=54×8,
Solution: a 1=4, a2=-2,
∴p(4.5) or (-2.5),
When the point p is lower than the x axis, the point does not exist.
P (4.5) or (-2.5).
(3) When the straight line y = x+m (m < 1) passes through the point D(0, -3),
∴-3=0+m,
∴m=-3;
When the straight line y=x+m has only one intersection with the parabola, x+m=x2-2x-3, that is, x2-3x-3-m=0,
δ= 9+4(3+m)= 0,
The solution is m=? 2 14.
To sum up, is the value of m 3 or? 2 14.