#### 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 .

## How do you find the vertex and axis of symmetry?

The Vertex Form of a quadratic function is given by: f(x)=a(x−h)2+k , where (h,k) is the Vertex of the parabola. x=h is the axis of symmetry. Use completing the square method to convert f(x) into Vertex Form.

## How do you find the equation of a parabola with two points and axis of symmetry?

Using the vertex form of a parabola f(x) = a(x – h)^{2} + k where (h,k) is the vertex of the parabola.The axis of symmetry is x = 0 so h also equals 0.a = 1.Substituting the a value into the first equation of the linear system:k = 3.f(1) = 4 = (1 – 0)^{2} + 3 = 1 + 3.f(2) = 7 = (2 – 0)^{2} + 3 = 4 + 3.

## 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.

## What is the equation to find the vertex?

Lesson SummaryGet the equation in the form y = ax2 + bx + c.Calculate -b / 2a. This is the x-coordinate of the vertex.To find the y-coordinate of the vertex, simply plug the value of -b / 2a into the equation for x and solve for y. This is the y-coordinate of the vertex.

## How do you find the vertex in standard form?

The standard form of a parabola is y=ax2++bx+c , where a≠0 . The vertex is the minimum or maximum point of a parabola. If a>0 , the vertex is the minimum point and the parabola opens upward. If a<0 , the vertex is the maximum point and the parabola opens downward.

## Where is the vertex on a graph?

Parabolas always have a lowest point (or a highest point, if the parabola is upside-down). This point, where the parabola changes direction, is called the “vertex”. If the quadratic is written in the form y = a(x – h)^{2} + k, then the vertex is the point (h, k).

## What is the definition of axis 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.

## How do you find the axis of symmetry of a hyperbola?

To determine the axes of symmetry we define the two straight lines y1=m1x+c1 and y2=m2x+c2. For the standard and shifted hyperbolic function, the gradient of one of the lines of symmetry is 1 and the gradient of the other line of symmetry is −1.

## 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.