Function – Parabola

 

Motivation:     y= ax² + bx + c, a  0 . What does its X-Y plot look like?

 

                      Other than using computer program to draw the graph and look at the plot,  some

                      properties of the graph can be obtained from some basic concept:

 

                      y = ax² + bx + c

                         = a( x² +   x ) + c

                         = a( x² + 2  x +  (  )² ) + c

                         = a( x +   )² + c -

                         = a( x +   )²  + 

 

                     Symmetry:      the graph is symmetric to  x =

 

                      If a > 0,   then its minimum value is   .  So, it should be look like

                                                

                                                         

                                     And  the minimum value happens when  x =  .

 

                      If a < 0,   then its maximum value is   .

                                                                     

                                       the maximum value happens when x =  .