Parabola is a common curve in mathematics, and its characteristic is that the distance from each point on the plane to a fixed point (focus) is equal to the distance from the parabola straight line (directrix). Parabola usually has two symmetrical ways, that is, it is symmetrical about X axis and Y axis. Here, the symmetry axis formula of parabola about x axis is deduced emphatically.

Consider a general parabolic equation: y = AX2+BX+C.

First of all, we need to find the symmetry axis of parabola, that is, the equation of X axis. Parabola is axisymmetrical about x, that is to say, any point (x, y) on the parabola is also a mirror image point (x, -y) on the x axis. Using this property, we can derive the formula of parabolic symmetry axis.

Consider a point (x, y) on a parabola and its mirror image point (x, -y) about the x axis. According to the parabolic equation, we have:

y=ax2+bx+c

y=ax2+bx+c

Adding the above two equations, we get:

0=2ax2+2c

Further simplification, the formula of parabola's symmetry axis about X axis is obtained:

x=c/？ a

This formula represents the x coordinate of the parabola's axis of symmetry about the x axis. This means that if the equation of parabola is y=ax? +bx+c, then its equation about the axis of X axis symmetry is x=? c/a .

This is the derivation of parabola's formula about X axis symmetry. Through this formula, we can easily determine the symmetry axis of parabola, so as to better understand and analyze the properties and behaviors of parabola.