1. Further Investigating Quadratics
L.O.
All pupils are confident with factorising and expanding brackets
All pupils understand why further methods for solving could be required
Most pupils can find further information from the completed square form
Some pupils can use the completed square form to sketch graphs

2. factorising and expanding brackets
Starter:
factorising and expanding brackets
Multiply out the brackets:
(x+3)(x+3)
(x+2)2
(x-5)2
Factorise:
x2 + 8x + 16
x2 - 12x + 36
x2 + 22x + 121
= x2 + 6x + 9
= x2 + 4x + 4
= x2 – 10x + 25
= (x + 4)²
= (x – 6)²
= (x + 11)²

3. Further Investigating Quadratics
L.O.
All pupils are confident with factorising and expanding brackets
All pupils understand why further methods for solving could be required
Most pupils can find further information from the completed square form
Some pupils can use the completed square form to sketch graphs

4. Main 1: Completing the Square x2 + 10x + 10 = 0
why further methods for solving could be required
find further information from the completed square form
Completing the Square
x2 + 10x + 10 = 0
Half the coefficient of x
(x + 5)2 – (5)² + 10 = 0
(x + 5)2 – = 0
Simplify
Special point
(-5, -15)
(x + 5)2 – 15 = 0
(x + 5)2 = 15
Solve
x + 5 = ± √15
x = - 5 ± √15
Make sure you have both + and – square root!

5. What is special about the ‘special point?
Main 1:
why further methods for solving could be required
find further information from the completed square form
Your go
Completing the Square – Your go
x2 - 8x + 5 = 0
Half the coefficient of x
(x - 4)2 – (-4)² + 5 = 0
(x - 4)2 – = 0
Simplify
Special point
(4, -11)
(x - 4)2 – 11 = 0
(x - 4)2 = 11
Solve
x - 4 = ± √11
x = 4 ± √11
Make sure you have both + and – square root!
Ext.
What is special about the ‘special point?

6. What do you do if you are given…
Main 1:
why further methods for solving could be required
find further information from the completed square form
What do you do if you are given…
Divide EVERYTHING by 3

7. Divide EVERYTHING by 3 Because: the coefficient of x² MUST be 1
Main 1:
why further methods for solving could be required
find further information from the completed square form
Divide EVERYTHING by 3 Because: the coefficient of x² MUST be 1

8. Complete the square to solve each of these equations.
Main 1:
why further methods for solving could be required
find further information from the completed square form
Complete the square to solve each of these equations.
Ext.
Draw an accurate sketch of each of these functions without using a table of values
Ext. 2
Use tables of values to check your graphs are correctly plotted

9. Further Investigating Quadratics
L.O.
All pupils are confident with factorising and expanding brackets
All pupils understand why further methods for solving could be required
Most pupils can find further information from the completed square form
Some pupils can use the completed square form to sketch graphs

10. Main 2: Minimum Points (x + 5)2 – 15 = 0 Minimum at (-5, -15)
further information from the completed square form
use the completed square form to sketch graphs
Minimum Points
(x + 5)2 – 15 = 0 Minimum at (-5, -15)
(x - 4)2 – 11 = 0 Minimum at (4, -11)
(x - 7)2 – 58 = 0 Minimum at (7, -58)
(x - p)2 + q = 0 Minimum at (p, q)

11. Main 2:
further information from the completed square form
use the completed square form to sketch graphs
Writing in completed square form (and write down the minimum point) Example

12. Main 2: Answers further information from the completed square form
use the completed square form to sketch graphs
Answers

13. Solving Quadratics by Completing the Square
Main 2:
further information from the completed square form
use the completed square form to sketch graphs
Solving Quadratics by Completing the Square
SECTIONS 1 & 3 – LEAVE IN SURD FORM! (Exact Solutions)

14. Main 2: Answers further information from the completed square form
use the completed square form to sketch graphs
Answers

15. Further Investigating Quadratics
L.O.
All pupils are confident with factorising and expanding brackets
All pupils understand why further methods for solving could be required
Most pupils can find further information from the completed square form
Some pupils can use the completed square form to sketch graphs

16. Plenary:

17. Plenary:
Answers

18. Further Investigating Quadratics
L.O.
All pupils are confident with factorising and expanding brackets
All pupils understand why further methods for solving could be required
Most pupils can find further information from the completed square form
Some pupils can use the completed square form to sketch graphs