It basically teaches us the overall concept of completing the square is to get an equation to vertex form, from standard.

 

 

Example 1: x2+4x+8 [Convert to vertex form]

Follow these simple steps:

 

Step #1: Group the x2 and x terms together                                (x2+4x)+8

Step #2: Complete the square inside the bracket                       (x2+4x+2-2)+8

Step #3: Close the brackets within to make it a                          ((x2+4x+2)-2)+8

perfect square trinomial

Step #4: Drop the brackets, and make sure the -2 is with -8    (x2+4x+2)-2+8

Step #5: Write the trinomial in binomial squared                         (x+2)^2+6

 

Therefore, the vertex is (-2,6) *Remember the positive 2 turns into a negative, refer to transformations of parabolas on the vertex*

 

Example 2: y= 4x2+16x+12

 

y= (4x2+16x)+12

y= 4(x2+4x)+12    *Remember to common factor*

y= 4(x2+4x+4-4)+12

y= 4(x+2)^2-16+12   *When we drop down the brackets we muliply the -4 and 4 which gives us -16* 

y= 4(x+2)^2-4

 

Therefore, the vertex is (-2,-4)

 

 

Now lets try!

 

a) -x-10x-9                                       b) 2x2+120x+75                                   c) y=-5x2-200x-120                  

 

 

 d) x2+9x+10

 

 

 

Answers: