10 Examples of Axis of Symmetry
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.
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.