Suppose ABC translates one unit downward at three points to form an equilateral triangle.
x? -a = 0, x = radical a.
The length of AB is two numbers a.
The height on the side of AB is a, according to the relationship between the length and height of an equilateral triangle.
2 (radical a)× (radical 3)/2 = a.
3a=a? ,a=3
At this time, the analytical formula of parabola is y=x? -3
Intersect with the x axis at points A(x 1, 0) and B(x2, 0).
Then the midpoint of these two points must be on the axis of symmetry of the parabola.
The midpoint coordinate of AB is ((x1+x2)/2,0).
So the equation of parabola symmetry axis is x=(x 1+x2)/2.
or
Let the analytical formula of parabola be y=a(x-x 1)(x-x2).
Y=ax after expansion? -a(x 1+x2)x+ax 1x2
The equation of symmetry axis is y=-b/(2a)=(x 1+x2)/2.