Axis of Symmetry Formula

Axis of Symmetry Formula:

Symmetry is the important concept in geometry that cuts the figure into two halves that are exact reflections of each other.

Axis of symmetry is a line that divides the object into two equal halves, hence creating a precise reflection of either side of the object. The word “symmetry” means balance. Symmetry can be applied to various contexts.

The axis of symmetry of a parabola is x=-b ⁄ 2a  for a quadratic function y =ax²+bx +c.

The straight line for every point on a given curve has a corresponding to another point such that the line connecting the two points is separated by the given line.

The axis of symmetry is the line perpendicular to the directrix that passes through the focus. The vertex is the midpoint of the segment whose endpoints are the focus and the intersection between the axis of symmetry and the direct point. 

The order of symmetry is defined as the number of times the figure coincides with itself as its rotates through 360° .You need to rotate the figure to 360 degrees. Once you rotate the figure up to 360 degrees, you are back to the original.

Example Problems on Area under the Axis of Symmetry

1) Find the axis of symmetry of the graph of   y =x²-6x+5.

Given that  y =x²-6x+5.

For a quadratic function , y =ax²+bx +c.

The axis of symmetry is x=-b / 2a 

a=1,b=-6 and c=5

 Substituting the values 

x=-(-6)/ 2(1)=6 / 2=3

2) Find the axis of symmetry of the graph of y=2x²+8x-3

Given that y=2x²+8x-3

For a quadratic function, y=ax²+bx+c

The axis of symmetry is x=-b / 2a  

Substituting the values 

x=-8 / 2(2)=-8 / 4=-2

3) If the axis of symmetry of the equation y=px²- 12x-5 is 2, then find the p value.

Given that y=px²-12-5

axis of symmetry is 2

For a quadratic function y=ax2+bx+c, the axis of symmetry is  x=-b / 2a.

a=p,b=-12,c=-5

–-b / 2a=2

12 / 2p=2

12=4p

12 / 4=p

Therefore, p=3.