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. We can see this axis of symmetry even in nature such as flowers, riverbanks, buildings, leaves, and so on.

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 line that bisects a two-dimensional figure. It is the line about which a figure is symmetrical. The axis of symmetry is the y-axis. A parabola is a two-dimensional curve that is the result of a quadratic equation.

How to find the equation of the axis of symmetry

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. Finding the axis of symmetry for a given polynomial is fairly simple. To find an axis of symmetry, start by checking the degree or largest exponential value of the polynomial. If the degree of your polynomial is 2, you can find the axis of symmetry by plugging the numbers directly into the axis of symmetry formula. Solve the formula and the answer you get is the x-intercept 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. For tips on solving graphically, read on! Did this summary help you?

The constant term 'c' does not affect the parabola. A parabola has one line 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.

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. It can be either horizontal or vertical, facing left or right. Now, we will discuss how to find the axis of symmetry of parabola from its standard and vertex forms of equations.

How to find the equation of the axis of symmetry

Every parabola has an axis of symmetry which is the line that divides the graph into two perfect halves. On this page, we will practice drawing the axis on a graph , learning the formula , stating the equation of the axis of symmetry when we know the parabola's equation. Explore how the graph and equation relate to the axis of symmetry , by using our interactive program below. There are two different formulas that you can use to find the axis of symmetry. One formula works when the parabola's equation is in vertex form and the other works when the parabola's equation is in standard form. Explore the relationship between the axis of symmetry and graph of a parabola by changing the values of a, b and c of the parabola plotter below.

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This article has been viewed , times. Maths Games. Essentially, in order to determine the axis of symmetry, we simply need to identify the vertex. About Us. Learn Axis Of Symmetry with tutors mapped to your child's learning needs. If the degree of the polynomial is higher than 2, use Method 2. Look for a point on the axis such that when a line is passed through it, the graph splits into two equal, mirrored halves. Axis of Symmetry Examples Example 1: Find the equation of the axis of symmetry of the given parabola. 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. Submit a Tip All tip submissions are carefully reviewed before being published. This is the key point to determine its equation. Yes, the line of symmetry and the axis of symmetry are the same. Follow Us. Online Courses Study Guides Flashcards.

Last Updated: January 5, Fact Checked. To create this article, volunteer authors worked to edit and improve it over time.

Support wikiHow Yes No. Axis of Symmetry of a Parabola A parabola is a two-dimensional curve that is the result of a quadratic equation. As always, if you have any questions or comments, please feel free to reach out to us! Our Mission. For example, if you have a triangle with vertices at -1, 2 , 3, 4 , and 5, -6 , then the axis of symmetry would be:. Look for a point on the axis such that when a line is passed through it, the graph splits into two equal, mirrored halves. Make two lines in the shape of a plus sign. Return to Math Sample Questions. Essentially, in order to determine the axis of symmetry, we simply need to identify the vertex. Draw the x- and y- axes. Check the degree of your polynomial.