2、
Solution: A (-b/2a,0) means A (-2c,0) A(-2c (0,c).
The distance between two points A and B is 2.
∴(-2c-0)？ +(c-0)？ =(2 root numbers 2)?
Solution: c = 2 * (root number 10)/5
Vertex a is on the x axis.
The quadratic function ∴ has only one intersection with the z axis.
Discriminant b? -4ac=0
∫b = 2ac
∴4a？ c？ -4ac=0
∵a≠0，c≠0
∴ac= 1
∴ The analytic formula of quadratic function is y=[ (root number 10)/4]x? +x+2* (root number 10)/5
Or y=-[ (root number 10)/4]x? +x-2* (root number 10)/5
3. Solution:
Angle ACB=90 degrees
∴C is on a circle with a diameter of AB.
The maximum value of this function is equal to 2.
The radius of a circle is 2.
∴ The diameter is 4, which means AB=4.
The abscissa of point A is 1.
The abscissa of point B is 5 or -3.
The abscissa of point C is half of the sum of the abscissas of ab.
That is, the abscissa of point C is 3 or-1.
∴ get:
A( 1，0) B(5，0) C(3，2)
Or a (1, 0) b (-3, 0) c (- 1, 2)
Two situations
Solve the resolution function as follows:
y=-x？ /2+3x-5/2 or y=-x? /2-x+3/2