( 1)y=ax^2+bx+c

=a(x^2+b/ax+c/a)

=a(x^2+b/ax+b^2/4a^2-b^2/4a^2+c/a)

=a(x+b/2ax)^2+(4ac-b^2)/4a

(2) Vertex coordinates

x=-b/2a y=(4ac-b^2)/4a

Axis of symmetry x=-b/2a

Opening: a>0, open:

A<0, open down.

(3)y=a(x- 1)^2+h=a(x- 1)(x-3)=a(x^2-2x-3)=ax^2-2ax-3a

=ax^2-2ax+a+h

Yes: a+h=-3a (coefficient to be determined)

-b/2a= 1

3=a( 1)(- 1)->A=-3 (after (2,3))

y=-3x^2+6x+9

(4) When the real root of the quadratic function is the y value of the quadratic function =0, the x coordinate value of the intersection of the function image and the x axis.

When there are several intersections between the function image and the X axis, there are several real roots. The real root is relative to the imaginary root, that is, when the value of the discriminant of the quadratic function is less than 0, the function does not intersect with the X axis, and there are a pair of imaginary roots at this time.