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# 10 Examples of Axis of Symmetry

October 18, 2023 written by Rida Mirza

Axis of symmetry is an important concept in mathematics. It represents a line that divides a figure or an equation into two mirror-image halves.

In this article, we will discuss ten examples of axis of symmetry in mathematics.

### Examples of Axis of Symmetry

These are 10 examples of axis of symmetry.

### 1: Parabola Vertex Form

Consider the quadratic equation: f(x) = (x – 3)^2 – 4. To find the axis of symmetry, we identify the value inside the parentheses, which is 3.

Axis of symmetry is the vertical line x = 3.

### 2: Graphing a Parabola

When graphing the equation y = x^2, you see that the axis of symmetry is the vertical line x = 0 (the y-axis).

### 3: Circle Equation

In the equation of a circle, (x – h)^2 + (y – k)^2 = r^2, the axis of symmetry is the horizontal line y = k.

### 4: Parabola Intercept Form

For the equation y = a(x – h)^2 + k, the axis of symmetry is the vertical line x = h.

### 5: Finding the Axis of Symmetry

Given the quadratic function f(x) = 2x^2 – 6x + 5, we find the axis of symmetry using the formula x = -b/2a.

In this case, x = -(-6) / (2 * 2) = 3/2.

### 6: Vertex Coordinates

Vertex of a parabola are used to identify the axis of symmetry.

For the parabola y = (x – 2)^2 – 3, the vertex is (2, -3), and the axis of symmetry is x = 2.

### 7: Real-World Applications

In a bridge design, if the left side is a mirror image of the right side, the axis of symmetry is the centerline of the bridge.

### 8: Geometry

In an isosceles triangle, where two sides and angles are congruent.

Axis of symmetry is the perpendicular bisector of the base.

### 9: Parabolic Mirror Focus

For a parabolic mirror used in telescopes or satellite dishes. Axis of symmetry passes through the focus point.

### 10: Art and Design

In graphic design, symmetry is often used for creating pleasing logos, illustrations, or architecture.

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