English | Español

Try our Free Online Math Solver!

Online Math Solver

 

 

 

 

 

 

 

 
 
 
 
 
 
 
 
 

 

 

 
 
 
 
 
 
 
 
 

Please use this form if you would like
to have this math solver on your website,
free of charge.


Quadratic Functions

Definition: A quadratic function is a function which can be put in the form

(General Form) or (Standard or Vertex Form )

For a quadratic functions or :

0) The domain of a quadratic function is

1) Graph : a (vertical) parabola

2) Opens up if

3) Opens down if

4) Vertex: with
and
5) The x- intercept (s) can be found by setting and solving for x .

6) The y- intercept an be found by setting and solving for y .

Remark: The above items can be used to sketch the graph of a quadratic function

Examples:

Remark: The conversion from vertex form to general from is very easy. For conversion from general form to vertex form
we use the method of Completing Square .

Example:

The Maximum and the Minimum of a Quadratic Function (Parabola):

As was discussed above, the vertex of a parabola is with

and

a) If the parabola opens up, the vertex will be the lowest point and we say that the parabola has the minimum value
of at .


b) If the parabola opes down, the vertex will be the highest point and we say that the parabola has the maximum
value of at .

Remark: The coordinates of the vertex can be found by a graphing calculator .

Examples:

Application:

Prev Next