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Axis of Symmetry of a Parabola

The graph of a quadratic function is a parabola. The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves. The axis of symmetry always passes through the vertex of the parabola . The $x$ -coordinate of the vertex is the equation of the axis of symmetry of the parabola.

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For a quadratic function in standard form, $y = a x^{2} + b x + c$ , the axis of symmetry is a vertical line $x = - \frac{b}{2 a}$ .

Example 1:

Find the axis of symmetry of the parabola shown.

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The $x$ -coordinate of the vertex is the equation of the axis of symmetry of the parabola.

The vertex of the parabola is $(2, 1)$ .

So, the axis of symmetry is the line $x = 2$ .

Example 2:

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

For a quadratic function in standard form, $y = a x^{2} + b x + c$ , the axis of symmetry is a vertical line $x = - \frac{b}{2 a}$ .

Here, $a = 1, b = - 6$ and $c = 5$ .

Substitute.

$x = - \frac{- 6}{2 (1)}$

Simplify.

$\begin{array}{l} x = \frac{6}{2} \\ = 3 \end{array}$

Therefore, the axis of symmetry is $x = 3$ .

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