Axis Of Symmetry Formula

Axis of Symmetry Formula

A shape can be divided into two identical sections by an imaginary straight line called the axis of symmetry, which makes one component the mirror image of the other. When the two parts are folded along the axis of symmetry, they become superimposed. The mirror line, or line of symmetry, is the name given to the straight line. This line may be horizontal, vertical, or diagonal.

When using the line of symmetry and the usual form of the equation, the Axis Of Symmetry Formula is applied to quadratic equations. The term “Axis Of Symmetry Formula” refers to a line that divides or splits any item into two halves that are mirror images of one another.

Any of the three types of axes—horizontal (x-axis), vertical (y-axis), or inclined line—can be used to divide the objects.

When a parabola is in either of two forms, the equation for the Axis Of Symmetry Formula can be represented as the Vertex form or the standard form.

Always, the parabola’s vertex is where the axis of symmetry is located. Thus, locating the vertex aids in our ability to determine where the axis of symmetry is located. The parabola’s Axis Of Symmetry Formula is x = -b/2a.

Both the axis and the line of symmetry are identical. They are fictitious lines that split a figure into two pieces that are mirror images of one another. The two parts of the figure superimpose when folded along this line.

Solved Examples

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

Solution:

Given,

y = px2 – 12x – 5

Axis of symmetry is x = 2

For a quadratic function in standard form, y=a

x2

+bx+c, the axis of symmetry is a vertical line,  x =

−b2a

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

According to the given,

-b/2a = 2

-(-12)/2p = 2

12 = 4p

12/4 = p

Therefore, p = 3