Completing the Square

Write in the form 

where and are integers.

Express in the form  , where and are integers.

The equation of a curve is 

Circle the coordinates of the turning point.

Write    in the form 

Write  in the form 

Write x² + 8x + 3  in the form (x + a)² - b.

Write  in the form 

Write    in the form  

Find the value of and the value of .
 

  = ............................................     
= ............................................     

Express in the form where andare integers.

is the curve with equation
The point is the maximum point on

Use your answer to part (a) to write down the coordinates of

Express  in the form  where  ,  and  are integers.

The function is such that       for

Express  in the form  where  and  are constants.

Write  in the form  where ,  and  are integers.

Express  in the form  where  and  are constants.

can be written in the form 

where and are positive numbers.

Work out the values of  and .

Find the turning point of    by completing the square.
 

( ...................... , .....................)