How to find the equation of the axis of symmetry

An axis of symmetry can be either horizontal, vertical, or diagonal. There are a few different equations that can be used to find the axis of symmetry for a given shape or object. In this blog post, we will go over a few of these equations and provide some examples to help you better understand how they work.

The axis of symmetry is an imaginary straight line that divides a shape into two identical parts, thereby creating one part as the mirror image of the other part. When folded along the axis of the symmetry, the two parts get superimposed. This line can be vertical, horizontal, or slanting. We can see this axis of symmetry even in nature such as flowers, riverbanks, buildings, leaves, and so on. We can observe this in the Taj Mahal, the iconic marble structure in India. The axis of symmetry is a straight line that makes the shape of the object symmetrical. The axis of symmetry creates the exact reflections on each of its sides.

How to find the equation of the axis of symmetry

A line of symmetry refers to a line that is drawn through the center of a shape so that it creates two identical halves. Each half is a mirror image of the other. Some shapes have one line of symmetry, like an isosceles triangle, and other shapes have many lines of symmetry. For example, a regular pentagon has 5 lines of symmetry. Not all shapes will have lines of symmetry however. Imagine the letter J. We cannot draw one line through the letter J with the result being two identical halves. Letters such as W , B , O , and Y do have lines of symmetry. The equation of a parabola creates an arc when it is graphed. This U shape has one line of symmetry, right down the middle of the arc. This line is referred to as the axis of symmetry. This line will split the parabola into two identical halves. Parabolas that are in vertex form will also have an axis of symmetry.

Now that we know the value of x is 1, we know that the axis of symmetry is also at 1. Imagine the letter J.

Last Updated: January 5, Fact Checked. To create this article, volunteer authors worked to edit and improve it over time. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed , times. Learn more The graph of a polynomial or function reveals many characteristics that would not be clear without a visual representation. One of these characteristics is the axis of symmetry: a vertical line on a graph that splits the graph into two symmetrical mirror images.

Home » Geometry » Symmetry » Axis of Symmetry. The axis of symmetry is an imaginary line that makes the shape symmetrical about it. In other words, it divides the shape into two halves such that each half is a mirror image of the other. If we fold and unfold an object along the axis of symmetry, the two sides are identical. The axis of symmetry is best studied in a parabola, while graphing a quadratic function. Thus, the axis of symmetry of a parabola is the line about which a parabola is symmetric. It always passes through its vertex. The axis of symmetry determines the form of the parabola.

How to find the equation of the axis of symmetry

The axis of symmetry is an imaginary straight line that divides a shape into two identical parts, thereby creating one part as the mirror image of the other part. When folded along the axis of the symmetry, the two parts get superimposed. This line can be vertical, horizontal, or slanting.

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Not Helpful 3 Helpful For example, a regular pentagon has 5 lines of symmetry. Cookies make wikiHow better. Once you have marked all the graph points, you can connect your dots smoothly to reveal a continuous graph of your polynomial. So, if you were to fold a figure along its axis of symmetry, the two halves would match up perfectly. Letters such as W , B , O , and Y do have lines of symmetry. Axis of Symmetry Questions. In the equation we can see that the value of h is represented by a 1, and the value of k is represented by a 2. The axis of symmetry is the midpoint of its two x-intercepts. How to. The axis of symmetry formula uses the standard form of the quadratic equation as well as the vertex form. Suppose the two points 3, 4 and 9, 4 are points on a parabola, then the vertex passes through the intercept which forms the midpoint of these given points.

A circle is thus said to be symmetric under rotation or to have rotational symmetry. The types of symmetries that are possible for a geometric object depend on the set of geometric transforms available, and on what object properties should remain unchanged after a transformation.

Not all shapes will have lines of symmetry however. Draw the graph of the polynomial. Saudi Arabia. Cookies make wikiHow better. A line of symmetry divides a figure into two equal mirror images, or halves. The axis of symmetry determines the form of the parabola. Identification of the Axis of Symmetry 8. Let us derive the equation of the axis of symmetry. If the degree of the polynomial is higher than 2, you will need to find the axis of symmetry by using a graph. Check the degree of your polynomial. However, the formula is slightly different. To identify the axis of symmetry of a parabola, one must first find the equation of the parabola. The axis of symmetry of a parabola can be horizontal or vertical. There are a few different equations that can be used to find the axis of symmetry for a given shape or object.