The purpose:

The square function is a function defined by a group of real numbers and presented 

according to the following model:  y=ax2+bx+c (a¹0, parameters  a, b, c)

2. The graph of the square function is called: Parabola.

3.The vertex of the parabola is called: extreme point 

-The extreme point is the point were the image is the lowest point 

(press for demonstration)

-this point is the maximum if it is the highest point- in this case it always conveys to a<0.

(press for demonstration)

The vertex point is:   ,    

4. Each image has two origins in the square function except the vertex since the vertex is the extreme point and there is one single origin at that point.

the correlation between the origins is :   x1 + x2 = -b/a     

5. The parabola has two branches which emerge from the vertex 

- the parabola is simmetrical and the equation of the simmetric axis is

x =  

6. (o, c) is the crossing point of the graph with the y -axis.

Practice

Draw a graph for each of the exercises according to the given data only- (x2 factor a)                

          
 a. the vertex at point          (-2, -16)  a = 1   (click here for the graphic answer)                  
 a. the vertex at point          (4, -3)   a = -1    (click here for the graphic answer)                       
  a. the vertex at point         (6, 0)   a = -2     (click here for the graphic answer)                      
  a. the vertex at point         (0,0)   a = 3       (click here for the graphic answer)                       

Click here for more exercises