Quadratic functions


Converting quadratic functions

Enter your quadratic function here. Instead of x², 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

By to the


Find a function

Degree of the function:
1 2 3 4 5

( 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 f_f(x)=a*x^2+b*x+c . This means, there is no x to a higher power than 2. The graph of a quadratic function is a parabola.