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Axis of Symmetry Formula

Axis of symmetry is a line that divides an object into two equal halves, thereby creating a mirror like reflection of either side of the object. The word symmetry implies balance. Symmetry can be applied to various contexts and situations. Symmetry is a key concept in geometry which cuts the figure into two halves that are exact reflections of each other, as shown in figure given below.

\[\large x = \frac{-b}{2a} for \: Quadratic \: Equation,\: y = ax^{2}+bx+c\]
Where,

a and b are coefficients of x2 and x respectively.
c is a constant term.

Axis of Symmetry

 

Example:

Find the axis of symmetry of the graph of y=$x^{2}$−6x+5, using the formula.

For a quadratic function in standard form, y=a$x^{2}$+bx+c, the axis of symmetry is a vertical line x = $\frac{-b}{2a}$
Here, a=1, b=−6 and c=5

Simplify.
x=6/2 = 3x
Therefore, the axis of symmetry is x=3.

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