Equation of axis of symmetry parabola calculator

Table of Contents Show

What are quadratic functions?
Algebra Examples
How do you find the equation of the axis of symmetry of a parabola?
How do you write the equation of the axis of symmetry?
What is the axis of symmetry of a parabola?
What is the equation of a parabola calculator?

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.

Algebra Examples

Find the Axis of Symmetry f(x)=(x-5)^2-4

Step 2

Use the vertex form, , to determine the values of , , and .

Step 3

Since the value of is positive, the parabola opens up.

Opens Up

Step 5

Find , the distance from the vertex to the focus.

Find the distance from the vertex to a focus of the parabola by using the following formula.

Substitute the value of into the formula.

Cancel the common factor of .

Cancel the common factor.

Step 6

The focus of a parabola can be found by adding to the y-coordinate if the parabola opens up or down.

Substitute the known values of , , and into the formula and simplify.

Step 7

Find the axis of symmetry by finding the line that passes through the vertex and the focus.

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 write the equation of the axis of symmetry?

The axis of symmetry formula is given as, for a quadratic equation with standard form as y = ax² + bx + c, is: x = -b/2a. If the parabola is in vertex form y = a(x-h)² + k, then the formula is x = h.

What is the axis of symmetry of a parabola?

The axis of symmetry is the vertical line that goes through the vertex of a parabola so the left and right sides of the parabola are symmetric. To simplify, this line splits the graph of a quadratic equation into two mirror images.

What is the equation of a parabola calculator?

The parabola equation in its vertex form is y = a(x - h)² + k , where: a — Same as the a coefficient in the standard form; h — x-coordinate of the parabola vertex; and. k — y-coordinate of the parabola vertex.