f(-2)= 1+m = 3 = = & gt； m=2
∴B(4,0),f(x)=- 1/2x+2
∵ parabola g (x) = ax 2+bx-2, whose image passes through a and B.
g(-2)=4a-2b-2=3
g(4)= 16a+4b-2=0
A= 1/2 and b=-3/2 are used to solve two equations simultaneously.
∴g(x)= 1/2x^2-3/2x-2
(2) Analysis: Move the parabola up by n units.
Then y = 1/2x 2-3/2x-2+n, and its image intersects with f(x) at p and with y axis at q.
1/2x^2-3/2x-2+n=- 1/2x+2==>； 1/2x^2-x-4+n=0
X 1= 1-√(9-2n)，x2= 1+√(9-2n)
Q(0，n-2)
∫PQ//x axis
Substitute X 1 and X2 into the straight line f(x) to get y 1=3/2+√(9-2n)/2, and y2=3/2-√(9-2n)/2.
Let y2 = 3/2-√ (9-2n)/2 = n-2 = = > n=5/2
The parabola rose by 5/2 units.
(3) Analysis: ∫f(X)=- 1/2x+2Y axis intersects with c (0,2), rotates around c by a certain angle, intersects with x axis, intersects with e, intersects with parabola symmetry axis, and intersects with x axis at f.
S(⊿EOC)=S(⊿EFD)/4
The symmetry axis of parabola is x=3/2, f (3/2,0).
The straight line f(x) rotates, that is, the point E moves to the left or right.
When point e is to the right of point f,
Obviously it is s (⊿ EOC) > S(⊿EFD), which contradicts the given conditions;
When point e coincides with point f,
S(⊿EFD)=0, which contradicts the given conditions;
When point e is between point o and point f,
Let e (x0,0)
The linear EC equation is y=-2/x0*x+2.
D(3/2，2-3/x0)
S(⊿EOC)= 1/2*OC*OE=x0
s(⊿efd)= 1/2*ef*df= 1/2(3/2-x0)|2-3/x0|
x0 = 1/8(3/2-x0)(3/x0-2)= = & gt； 4x0^2+4x0-3=0==>； X0= 1/2 or x0=-3/2 (s).
When e (1/2,0), S(⊿EOC)=S(⊿EFD)/4 is satisfactory.
At this time, the analytical formula of the straight line EC is y=-4x+2.
When point e coincides with point o,
S(⊿EOC)=0, which contradicts the given conditions;
When point e is to the left of o,
Make E(-x0，0)(x0 & gt； 0)
The linear EC equation is y=2/x0*x+2.
D(3/2，2+3/x0)
S(⊿EOC)= 1/2*OC*OE=x0
s(⊿efd)= 1/2*ef*df= 1/2(3/2+x0)(2+3/x0)
x0 = 1/8(3/2+x0)(3/x0+2)= = & gt； 4x0^2-4x0-3=0==>； X0=3/2 or x0=- 1/2 (exclusive)
When e (-3/2,0), S(⊿EOC)=S(⊿EFD)/4 is very satisfactory.
At this time, the analytical formula of the straight line EC is y=4/3x+2.
To sum up, the analytical formula of linear EC is y=-4x+2 or y=4/3x+2.