In mathematics, an imaginary line that separates a shape into two identical parts can be defined as the axis of symmetry. This line is a straight line which can either be a horizontal straight line or a vertical straight line and a lateral line. The different shapes of geometry have different numbers of symmetry. For example, a rectangle will have 2 symmetrical lines, a square has four symmetrical lines, a circle has numerous, or you can say infinite numbers of these lines, a parallelogram consists of no lines of symmetry. The axis of symmetry can be observed in various monuments as well, such as the Taj Mahal (one of the eight wonders of the world). In this article, we will try to cover some basic concepts regarding the axis of symmetry such as types of equations, properties of it, and do a detailed analysis about them.
Types of equations in Axis of Symmetry
As mentioned above, the axis of symmetry is an imaginary line that separates a shape into two identical parts. The formula for the axis of symmetry can be used in quadratic equations to find standard form; it also helps to find the symmetry of a parabola. The lines of the axis vary on the basis of shapes, some of these lines are horizontal lines, lateral lines, and inclined or vertical lines. Basically, there are two types of equations found in the axis of symmetry. The following points analyses the types with solved examples.
- The first form is the standard form which is given by the ax. ax + bx + c = 0 where c can be regarded as the constant, x is the coefficient and ‘a’ and ‘b’ are defined as the coefficient of ‘x’. The formula given for it is, x = -b/2a. Let us solve some examples so that the topic becomes clearer to you.
Example 1: Using the formula of the axis of symmetry, find the value of x if the quadratic equation is, x.x + 2x + 3?
Given that,
Quadratic equation = x.x + 2x + 3,
Now using the formula of axis of symmetry, x = -b/2a;
X = – 2/ 2 * 1
X = -1
Therefore, the axis of symmetry for the given quadratic equation is equivalent to, -1.
Example 2: Using the formula of the axis of symmetry, find the value of x if the quadratic equation is, x.x + 6x + 3?
Given that,
Quadratic equation = x.x + 2x + 3,
Now using the formula of axis of symmetry, x = -b/2a;
X = – 6/ 2 * 1
X = -3
Therefore, the axis of symmetry for the given quadratic equation is equivalent to, -3.
- The second form is the vertex form where the value of x is equivalent to h where the formula is given by h = -b/2a. The quadratic equation given for the vertex form is, y = a ( x-h ) (x-h) + k . Let us solve some examples so that the topic becomes clearer to you.
Example 1: find the axis of symmetry of a shape, where y = 2x.x
Given that,
Y = 2x.x
Using the formula, h = -b/2a,
H = 0 / 2 * 2
H = 0/4
H = 0
Therefore, the axis of symmetry for the given shape is = 0
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