{"id":71180,"date":"2021-04-08T13:32:34","date_gmt":"2021-04-08T18:32:34","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=71180"},"modified":"2026-05-08T13:38:41","modified_gmt":"2026-05-08T18:38:41","slug":"axis-of-symmetry","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/axis-of-symmetry\/","title":{"rendered":"Axis of Symmetry Overview"},"content":{"rendered":"

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.<\/p>\n

\"three<\/p>\n

For example, a regular pentagon has 5 lines of symmetry. Not all shapes will have lines of symmetry however. Imagine the letter J<\/strong>. We cannot draw one line through the letter J<\/strong> with the result being two identical halves. Letters such as W<\/strong>, B<\/strong>, O<\/strong>, and Y<\/strong> do have lines of symmetry.<\/p>\n

\"W,<\/p>\n

Axis of Symmetry Sample Questions<\/a><\/div>\n

The equation of a parabola<\/a> 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<\/strong>.<\/p>\n

Axis of Symmetry Formula<\/h3>\n

When a parabola is graphed in standard form, we can use the formula \\(x=\\frac{-b}{2a}\\) in order to locate the axis of symmetry. Remember that when an equation is in standard form it appears as \\(y=ax^2+bx+c\\). We can take the values of a<\/em> and b<\/em> and plug them into the formula \\(x=\\frac{-b}{2a}\\) in order to solve for x<\/em>.<\/p>\n

\"\"<\/p>\n

For example, if we are given the equation for a parabola in standard form such as \\(y=x^2+4x+3\\), we know that \\(a=1\\), \\(b=4\\), and \\(c=3\\). From this point we can plug in the value of a<\/em> and b<\/em> into the formula \\(x=\\frac{-b}{2a}\\) in order to determine the axis of symmetry. The formula becomes \\(x=\\frac{-(4)}{2(1)}\\) which simplifies to \\(x=-2\\). This means that the axis of symmetry is the vertical line passing through \\(x=-2\\). This line will split the parabola into two identical halves.<\/p>\n

Parabolas that are in vertex form will also have an axis of symmetry. However, the formula is slightly different. When a parabola is given in vertex form, it appears as \\(y=a(x-h)^2+k\\), where h<\/em> and k<\/em> represent the ordered pair at the vertex of the graph. In other words, \\((h,k)\\) is the base point or the top point on the arc. This means that if a line is drawn vertically through this vertex, it will divide the parabola into two equal halves. Essentially, in order to determine the axis of symmetry, we simply need to identify the vertex. The formula for the axis of symmetry for a parabola in vertex form is \\(x=h\\).<\/p>\n

\"graphed<\/div>\n

For example, if you are given \\(y=(x-1)^2+2\\) as the equation of a parabola in vertex form, and you need to determine the axis of symmetry, you first need to identify the vertex, and then the value of h<\/em>. The vertex is \\((h,k)\\) when in vertex form \\((y=a(x-h)^2+k)\\). In the equation we can see that the value of h<\/em> is represented by a 1, and the value of k<\/em> is represented by a 2. This tells us that the vertex is at the point \\((1,2)\\). Now that we know the value of x<\/em> is 1, we know that the axis of symmetry is also at 1. The vertical line drawn at \\(x=1\\) is the axis of symmetry.<\/p>\n

\"graphed<\/p>\n\"Click<\/a>\n

Axis of Symmetry Sample Questions<\/h2>\n

Here are a few sample questions going over axis of symmetry.
\n\n\t\t\t\t

\n\t\t\t\t\tQuestion #1:<\/strong>\n\t\t\t\t\t

 
\nHow many lines of symmetry can be drawn on a regular pentagon? <\/p>\n<\/div>\n\t\t\t\t\t

3<\/div>
4<\/div>
5<\/div>
6<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t
\n\t\t\t\t\t\tAnswer:<\/strong>

A line of symmetry divides a figure into two equal mirror images, or halves. For a pentagon, there are five different lines of symmetry.<\/p>\n

\"A<\/p>\n<\/div>\n\t\t\t\t\t\t

\n\t\t\t\t\tQuestion #2:<\/strong>\n\t\t\t\t\t

 
\nWhat is the formula for the axis of symmetry for a parabola that is in standard form?<\/p>\n<\/div>\n\t\t\t\t\t

\\(x=\\)\\(\\:\\frac{-b}{2a}\\)<\/span><\/div>
\\(x=\\)\\(\\:\\frac{b}{2a}\\)<\/span><\/div>
\\(x=\\)\\(\\:\\frac{-b}{-2a}\\)<\/span><\/div>
\\(x=\\)\\(\\:\\frac{2b}{3a}\\)<\/span><\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t