#### How to find the equation of the axis of symmetry

## How do you find the equation of the axis of symmetry of a parabola?

The axis of symmetry always passes through the vertex of the parabola . The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola. For a quadratic function in standard form, y=ax2+bx+c , the axis of symmetry is a vertical line x=−b2a .

## What are the axes of symmetry?

A line through a shape so that each side is a mirror image. When the shape is folded in half along the axis of symmetry, then the two halves match up.

## How do you draw the axis of symmetry?

The following steps are used to construct AB of length 7.3 cm and its axis of symmetry.Draw a line segment AB of length 7.3 cm.Now, take A as centre and draw a circle by using the compass. With the same radius, draw another circle using compass taking B as centre. Now, join CD.So, CD is the axis of symmetry.

## What is the axis of symmetry examples?

The two sides of a graph on either side of the axis of symmetry look like mirror images of each other. Example: This is a graph of the parabola y = x^{2} – 4x + 2 together with its axis of symmetry x = 2. The axis of symmetry is the red vertical line.

## What is the equation of a parabola?

Given the focus (h,k) and the directrix y=mx+b, the equation for a parabola is (y – mx – b)^2 / (m^2 +1) = (x – h)^2 + (y – k)^2.

## How do I find the line of symmetry?

To find the line of symmetry algebraically, you need to identify if the equation is written in standard form or vertex form. Standard form is y = ax^2 + bx + c, where a, b, and c equal all real numbers. You can use the formula x = -b / 2a to find the line of symmetry.

## What is the axis of symmetry of a square?

Another way to think about the symmetric function is that if the shape were to be folded in half over the axis, the two halves would be identical: the two halves are each other’s mirror images. Thus a square has four axes of symmetry, because there are four different ways to fold it and have the edges all match.

## Can the axis of symmetry be negative?

When a<0, the parabola opens downward. When a=0, the graph is not a parabola but a line. In a parabola the axis of symmetry is x= -b/2a. When ‘a’ was positive the axis of symmetry was negative, and when a was negative the axis of symmetry was positive.

## Can the axis of symmetry be 0?

A parabola’s axis of symmetry always goes through the vertex of the parabola. In other words, it is a vertical line that goes through the x-coordinate of the vertex. Therefore, the equation of the axis of symmetry for this parabola is x = 0.

## What is y axis symmetry?

A graph is said to be symmetric about the y -axis if whenever (a,b) is on the graph then so is (−a,b) . A graph is said to be symmetric about the origin if whenever (a,b) is on the graph then so is (−a,−b) . Here is a sketch of a graph that is symmetric about the origin.