Completing the Square

Completing the Square2e.g. ( ) 6 7 0i x x

Completing the Square2 6 7x x move the constant

2e.g. ( ) 6 7 0i x x

Completing the Squaremove the constant

2 2 26 3 7 3x x add half the coefficient of ‘x’ squared

2 6 7x x

2e.g. ( ) 6 7 0i x x

Completing the Square

2 6 9 16x x

move the constant

add half the coefficient of ‘x’ squared

23 16x factorise to a perfect square

2 2 26 3 7 3x x

2 6 7x x

2e.g. ( ) 6 7 0i x x

Completing the Square

2 6 9 16x x

3 4x

move the constant

add half the coefficient of ‘x’ squared

23 16x factorise to a perfect square

2 2 26 3 7 3x x

2 6 7x x

2e.g. ( ) 6 7 0i x x

Completing the Square

2 6 9 16x x

3 4x

7 or 1x x

move the constant

add half the coefficient of ‘x’ squared

23 16x factorise to a perfect square

3 4x

2 2 26 3 7 3x x

2 6 7x x

2e.g. ( ) 6 7 0i x x

2( ) 0ii ax bx c

2( ) 0ii ax bx c

2 0b cx xa a

2( ) 0ii ax bx c

2 0b cx xa a

2 b cx xa a

2( ) 0ii ax bx c

2 0b cx xa a

2 b cx xa a

2 2

2

2 2b b c bx xa a a a

2( ) 0ii ax bx c

2 0b cx xa a

2 b cx xa a

2 2

2

2 2b b c bx xa a a a

2 2

22 4b c bxa a a

2

24

4b ac

a

2( ) 0ii ax bx c

2 0b cx xa a

2 b cx xa a

2 2

2

2 2b b c bx xa a a a

2 2

22 4b c bxa a a

2

24

4b ac

a

2 42 2b b acxa a

2( ) 0ii ax bx c

2 0b cx xa a

2 b cx xa a

2 2

2

2 2b b c bx xa a a a

2 2

22 4b c bxa a a

2

24

4b ac

a

2 42 2b b acxa a

2 42

b b acxa

2( ) 6 6 0iii x x

2( ) 6 6 0iii x x

23 0x

2( ) 6 6 0iii x x

23 0x 3

2( ) 6 6 0iii x x

23 0x 3

3 3 3 3 0x x

2( ) 6 6 0iii x x

23 0x 3

3 3 3 3 0x x

3 3 or 3 3x x

2( ) 6 6 0iii x x

23 0x

Exercise 1I; 1adh, 2ch, 3adg, 4bdfh, 5bdf, 6adg, 7bc, 8*

3

3 3 3 3 0x x

3 3 or 3 3x x