National 6 Mathematics
Pupil Revision Booklet
Completing the Square
Please complete the questions and mark
using the answers. If you are stuck please ask
your teacher or drop into a supported study.
Completing The Square
1.
2.
Write each of the following quadratic expressions in the form
a ( x b )2  c :
(a)
x2 6x 3
(b)
x2 5x 1
(c)
3x2 12x 2
(d )
2x2 6x 4
(e)
4 8x x2
(f )
1 4x 2x2
Show that the function
form
f (x)  2x2  16x 7 can be written in the
f (x)  a ( x p ) 2  q and write down the values of a , p and q.
Hence state the minimum value of the function and the corresponding value of x .
Completing the Square - Answers
(a)
(x 3)2 12
(b)
(x  5 )2 5 1
2
(d )
2(x  3 )2 8 1
2
(e)
(c)
20 (x 4)2
(a)
(f )
3 2(x 1)2
2
or (x 4)2 20
2.
3(x 2)2 10
4
f (x) 2(x 4)2 25
min value of -25 @
x=4
,
a 2, p 4, q 25
or 2(x 1)2 3