a+b=5
a-b= 1
Solve the equation to get a = 3 and b = 2.
The analytical formula of this parabola is y=3x? +2 times
The symmetry axis is x=-b/2a=-2/6=- 1/3.
Solution 2: Put X = 0 and Y = 0； respectively; x=2，y = 8； X=-2, y=0 and y=ax? +bx+c can get the equations about a, b and c;
c=0
4a+2b+c=8
4a-2b+c=0
Solve the equation to get a = 1, b = 2, c = 0.
The analytical formula of this parabola is y=x? +2 times
Solution 3:
(1): replace y=ax with X =-2 and Y = 4? Get:
4a=4
a= 1
(2): The analytical formula of parabola is y=x?
When x=-3 and y=(-3)? =9
(3): When x=- 1, y=(- 1)? = 1, so the parabola does not pass through the point (-1, 2).
Solution 4: Substitute X =-2 and Y = 0 into y=x? -2x+m available:
4+4+m=0
m=-8
The analytical formula of parabola is y=x? -2x-8, let y=0 to get the equation:
x？ -2x-8=0
(x+2)(x-4)=0
X+2=0 or x-4=0.
X=-2 or x=4.
The coordinate of another intersection of parabola and X axis is (4,0).
Solve five problems:
(1): x = 4 and y = 0；, respectively; X= 1, y=3 and y=-x? +bx+c can get the equations about b and c;
- 16+4b+c=0
- 1+b+c=3
Solve the equations to get b = 4 and c = 0.
The analytical formula of parabola is y=-x? +4x
Make the analytical expression of parabola into vertex;
y=-x？ +4x
=-(x？ -4x+4)+4
=-(x-2)？ +4
The symmetry axis is x=2, and the vertex coordinates are (2,4).