For y=x? The abscissas of the two intersections of the +bx+c image and the x axis are X 1 and X2, that is, x? The two roots of +bx+c=0 are X 1 and X2.

X 1=(-b+√(b？ -4c))/2

X2=(-b-√(b？ -4c))/2

For x? +b？ x+20=0

X3=(-b？ +√(b^4-80))/2

X4=(-b？ -√(b^4-80))/2

It doesn't matter which item after the root symbol is+or-.

Because X2-X3=X 1-X4=3.

(-b+√(b？ -4c))/2-[-b？ +√(b^4-80))/2]=3...............................( 1)

(-b-√(b？ -4c))/2- [-b？ -√(b^4-80))/2]=3................................(2)

( 1)+(2)= -2b+2b？ = 12 is b? -b-6=0, that is, (b-3)(b+2)=0.

So b=3 or b=-2. When b=-2, for x? +b？ X+20=0 is X? +4x+20=0 has no real root.

So b=3 brings 9-4c = 1 and c=2.

So the analytical formula is y=x? +3x+2

So we get the vertex coordinates (-3/2,-1/4).

Calculation is over.