Find the equation of the axis of symmetry calculator

Table of Contents Show

What are quadratic functions?
How do you find the equation of the axis of symmetry?
How do you find the equation of the vertex and axis of symmetry?

Converting quadratic functions

Enter your quadratic function here. Instead of x�, you can also write x^2.

Get the following form:
Vertex form
Normal form
Factorized form

Get a quadratic function from its roots

Enter the roots and an additional point on the Graph. Mathepower finds the function and sketches the parabola.

Roots at and

Further point on the Graph:

P(|)

Calculate a quadratic function given the vertex point

Enter the vertex point and another point on the graph.

Vertex point: (|)

Further point: (|)

Computing a quadratic function out of three points

Enter three points. Mathepower calculates the quadratic function whose graph goes through those points.

Point A(|)

Point B(|)

Point C(|)

Find the roots

Enter the function whose roots you want to find.

Hints: Enter as 3*x^2 ,
as (x+1)/(x-2x^4) and
as 3/5.

Transforming functions

Enter your function here.

How shall your function be transformed?

By in x-direction

By in y-direction

By to the

Find a function

Degree of the function:

( The degree is the highest power of an x. )

Symmetries:
axis symmetric to the y-axis
point symmetric to the origin

y-axis intercept

Roots / Maxima / Minima /Inflection points:
at x=
at x=
at x=
at x=
at x=

Characteristic points:
at |)
at |)
at |)
at (|)
at (|)

Slope at given x-coordinates:
Slope at x=
Slope at x=
Slope at

What are quadratic functions?

Quadratic functions are functions of the form . This means, there is no x to a higher power than . The graph of a quadratic function is a parabola.

The graph of a quadratic function is a parabola. The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves. 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 = a x 2 + b x + c , the axis of symmetry is a vertical line x = − b 2 a .

Example 1:

Find the axis of symmetry of the parabola shown.

The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola.

The vertex of the parabola is ( 2 , 1 ) .

So, the axis of symmetry is the line x = 2 .

Example 2:

Find the axis of symmetry of the graph of y = x 2 − 6 x + 5 using the formula.

For a quadratic function in standard form, y = a x 2 + b x + c , the axis of symmetry is a vertical line x = − b 2 a .

Here, a = 1 , b = − 6 and c = 5 .

Substitute.

x = − − 6 2 ( 1 )

Simplify.

x = 6 2 = 3

Therefore, the axis of symmetry is x = 3 .

How do you find the equation of the axis of symmetry?

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 equation of 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.