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Quadratics and Completing the
Square
Quadratics and Completing the
Square
e.g. 2
Sketch the parabola 8 12y x x  
Quadratics and Completing the
Square
e.g. 2
Sketch the parabola 8 12y x x  
2
8 12y x x  
Quadratics and Completing the
Square
e.g. 2
Sketch the parabola 8 12y x x  
2
8 12y x x  
 
2
4 4x  
Quadratics and Completing the
Square
e.g. 2
Sketch the parabola 8 12y x x  
2
8 12y x x  
 
2
4 4x  
 vertex is 4, 4  
Quadratics and Completing the
Square
e.g. 2
Sketch the parabola 8 12y x x  
2
8 12y x x  
 
2
4 4x  
 vertex is 4, 4  
x intercepts
Quadratics and Completing the
Square
e.g. 2
Sketch the parabola 8 12y x x  
2
8 12y x x  
 
2
4 4x  
 vertex is 4, 4  
x intercepts  
2
4 4 0x   
Quadratics and Completing the
Square
e.g. 2
Sketch the parabola 8 12y x x  
2
8 12y x x  
 
2
4 4x  
 vertex is 4, 4  
x intercepts  
2
4 4 0x   
 
2
4 4x  
Quadratics and Completing the
Square
e.g. 2
Sketch the parabola 8 12y x x  
2
8 12y x x  
 
2
4 4x  
 vertex is 4, 4  
x intercepts  
2
4 4 0x   
 
2
4 4x  
4 2
4 2
x
x
  
  
Quadratics and Completing the
Square
e.g. 2
Sketch the parabola 8 12y x x  
2
8 12y x x  
 
2
4 4x  
 vertex is 4, 4  
x intercepts  
2
4 4 0x   
 
2
4 4x  
6 or 2x x   
4 2
4 2
x
x
  
  
Quadratics and Completing the
Square
e.g. 2
Sketch the parabola 8 12y x x  
2
8 12y x x  
 
2
4 4x  
 vertex is 4, 4  
x intercepts  
2
4 4 0x   
 
2
4 4x  
6 or 2x x   
   
intercepts are
6,0 and 2,0
x
 
4 2
4 2
x
x
  
  
Quadratics and Completing the
Square
e.g. 2
Sketch the parabola 8 12y x x  
2
8 12y x x  
 
2
4 4x  
 vertex is 4, 4  
x intercepts  
2
4 4 0x   
 
2
4 4x  
6 or 2x x   
   
intercepts are
6,0 and 2,0
x
 
4 2
4 2
x
x
  
  
(ii) Write down the quadratic with roots 2 and 8 and vertex (5,3)
Quadratics and Completing the
Square
e.g. 2
Sketch the parabola 8 12y x x  
2
8 12y x x  
 
2
4 4x  
 vertex is 4, 4  
x intercepts  
2
4 4 0x   
 
2
4 4x  
6 or 2x x   
   
intercepts are
6,0 and 2,0
x
 
4 2
4 2
x
x
  
  
(ii) Write down the quadratic with roots 2 and 8 and vertex (5,3)
  2
5 3y k x  
Quadratics and Completing the
Square
e.g. 2
Sketch the parabola 8 12y x x  
2
8 12y x x  
 
2
4 4x  
 vertex is 4, 4  
x intercepts  
2
4 4 0x   
 
2
4 4x  
6 or 2x x   
   
intercepts are
6,0 and 2,0
x
 
4 2
4 2
x
x
  
  
(ii) Write down the quadratic with roots 2 and 8 and vertex (5,3)
  2
5 3y k x  
    2
2,0 : 0 2 5 3k  
Quadratics and Completing the
Square
e.g. 2
Sketch the parabola 8 12y x x  
2
8 12y x x  
 
2
4 4x  
 vertex is 4, 4  
x intercepts  
2
4 4 0x   
 
2
4 4x  
6 or 2x x   
   
intercepts are
6,0 and 2,0
x
 
4 2
4 2
x
x
  
  
(ii) Write down the quadratic with roots 2 and 8 and vertex (5,3)
  2
5 3y k x  
    2
2,0 : 0 2 5 3k  
9 3
1
3
k
k
 
 
Quadratics and Completing the
Square
e.g. 2
Sketch the parabola 8 12y x x  
2
8 12y x x  
 
2
4 4x  
 vertex is 4, 4  
x intercepts  
2
4 4 0x   
 
2
4 4x  
6 or 2x x   
   
intercepts are
6,0 and 2,0
x
 
4 2
4 2
x
x
  
  
(ii) Write down the quadratic with roots 2 and 8 and vertex (5,3)
  2
5 3y k x  
    2
2,0 : 0 2 5 3k  
9 3
1
3
k
k
 
 
  21
5 3
3
y x   
Quadratics and Completing the
Square
e.g. 2
Sketch the parabola 8 12y x x  
2
8 12y x x  
 
2
4 4x  
 vertex is 4, 4  
x intercepts  
2
4 4 0x   
 
2
4 4x  
6 or 2x x   
   
intercepts are
6,0 and 2,0
x
 
4 2
4 2
x
x
  
  
(ii) Write down the quadratic with roots 2 and 8 and vertex (5,3)
  2
5 3y k x  
    2
2,0 : 0 2 5 3k  
9 3
1
3
k
k
 
 
  21
5 3
3
y x   
 21
10 16
3
y x x   
Quadratics and the Discriminant
Quadratics and the Discriminant
2
4b ac  
Quadratics and the Discriminant
2
4b ac  
vertex ,
2 4
b
a a
    
 
Quadratics and the Discriminant
2
4b ac  
vertex ,
2 4
b
a a
    
 
zeroes
2
b
a
  

Quadratics and the Discriminant
2
4b ac  
vertex ,
2 4
b
a a
    
 
zeroes
2
b
a
  

Note: if 0, no interceptsx 
Quadratics and the Discriminant
2
4b ac  
vertex ,
2 4
b
a a
    
 
zeroes
2
b
a
  

Note: if 0, no interceptsx 
0, one interceptx 
Quadratics and the Discriminant
2
4b ac  
vertex ,
2 4
b
a a
    
 
zeroes
2
b
a
  

Note: if 0, no interceptsx 
0, one interceptx 
0, two interceptsx 
Quadratics and the Discriminant
2
4b ac  
vertex ,
2 4
b
a a
    
 
zeroes
2
b
a
  

Note: if 0, no interceptsx 
0, one interceptx 
0, two interceptsx 
2
e.g. Sketch the parabola 8 12y x x  
Quadratics and the Discriminant
2
4b ac  
vertex ,
2 4
b
a a
    
 
zeroes
2
b
a
  

Note: if 0, no interceptsx 
0, one interceptx 
0, two interceptsx 
  2
8 4 1 12
16
  

2
e.g. Sketch the parabola 8 12y x x  
Quadratics and the Discriminant
2
4b ac  
vertex ,
2 4
b
a a
    
 
zeroes
2
b
a
  

Note: if 0, no interceptsx 
0, one interceptx 
0, two interceptsx 
  2
8 4 1 12
16
  

2
e.g. Sketch the parabola 8 12y x x  
8 16
vertex ,
2 4
     
 
Quadratics and the Discriminant
2
4b ac  
vertex ,
2 4
b
a a
    
 
zeroes
2
b
a
  

Note: if 0, no interceptsx 
0, one interceptx 
0, two interceptsx 
  2
8 4 1 12
16
  

2
e.g. Sketch the parabola 8 12y x x  
8 16
vertex ,
2 4
     
 
 4, 4  
Quadratics and the Discriminant
2
4b ac  
vertex ,
2 4
b
a a
    
 
zeroes
2
b
a
  

Note: if 0, no interceptsx 
0, one interceptx 
0, two interceptsx 
  2
8 4 1 12
16
  

2
e.g. Sketch the parabola 8 12y x x  
8 16
vertex ,
2 4
     
 
 4, 4  
Exercise 8B; 1cfi, 2bd, 3c, 4b, 6bei, 10b,
11d, 16, 17, 20*
Exercise 8C; 1adg, 2adg, 3ad, 5ac, 8ac,
10, 13*

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Destaque

11 x1 t09 07 rates of change (2012)
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11 x1 t10 04 maximum & minimum problems (2012)
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11 x1 t09 06 quotient & reciprocal rules (2013)
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11 x1 t09 01 limits & continuity (2012)
11 x1 t09 01 limits & continuity (2012)11 x1 t09 01 limits & continuity (2012)
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11 x1 t09 02 first principles (2013)
11 x1 t09 02 first principles (2013)11 x1 t09 02 first principles (2013)
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11 x1 t09 05 product rule (2012)
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11 x1 t09 03 rules for differentiation (2012)
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11 x1 t10 03 equations reducible to quadratics (2013)
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11 x1 t10 05 the discriminant (2013)
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11 x1 t09 02 first principles (2012)
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11 x1 t10 06 sign of a quadratic (2013)
11 x1 t10 06 sign of a quadratic (2013)11 x1 t10 06 sign of a quadratic (2013)
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11 x1 t10 08 quadratic identities (2013)
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11 x1 t09 04 chain rule (2012)
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Destaque (20)

11 x1 t09 07 rates of change (2012)
11 x1 t09 07 rates of change (2012)11 x1 t09 07 rates of change (2012)
11 x1 t09 07 rates of change (2012)
 
11 x1 t10 04 maximum & minimum problems (2012)
11 x1 t10 04 maximum & minimum problems (2012)11 x1 t10 04 maximum & minimum problems (2012)
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11 x1 t09 06 quotient & reciprocal rules (2013)
11 x1 t09 06 quotient & reciprocal rules (2013)11 x1 t09 06 quotient & reciprocal rules (2013)
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11 x1 t09 01 limits & continuity (2012)
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11 x1 t09 02 first principles (2013)
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11 x1 t09 05 product rule (2012)
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11 x1 t09 03 rules for differentiation (2012)
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11 x1 t10 03 equations reducible to quadratics (2013)
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11 x1 t09 01 limits & continuity (2013)
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11 x1 t09 01 limits & continuity (2013)
 
11 x1 t10 01 graphing quadratics (2013)
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11 x1 t10 01 graphing quadratics (2013)
 
11 x1 t10 05 the discriminant (2013)
11 x1 t10 05 the discriminant (2013)11 x1 t10 05 the discriminant (2013)
11 x1 t10 05 the discriminant (2013)
 
11 x1 t09 02 first principles (2012)
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11 x1 t09 02 first principles (2012)
 
11 x1 t10 06 sign of a quadratic (2013)
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11 x1 t10 08 quadratic identities (2013)
11 x1 t10 08 quadratic identities (2013)11 x1 t10 08 quadratic identities (2013)
11 x1 t10 08 quadratic identities (2013)
 
11 x1 t09 04 chain rule (2012)
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11X1 T09 06 quotient and reciprocal rules (2010)
11X1 T09 06 quotient and reciprocal rules (2010)11X1 T09 06 quotient and reciprocal rules (2010)
11X1 T09 06 quotient and reciprocal rules (2010)
 
11 x1 t10 07 sum & product of roots (2013)
11 x1 t10 07 sum & product of roots (2013)11 x1 t10 07 sum & product of roots (2013)
11 x1 t10 07 sum & product of roots (2013)
 
11 x1 t09 08 implicit differentiation (2013)
11 x1 t09 08 implicit differentiation (2013)11 x1 t09 08 implicit differentiation (2013)
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11 x1 t08 01 radian measure (13)
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11 x1 t15 06 roots & coefficients (2013)
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12 x1 t01 01 log laws (2013)
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X2 t02 01 factorising complex expressions (2013)
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11 x1 t16 06 derivative times function (2013)
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11 x1 t16 05 volumes (2013)
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Mais de Nigel Simmons (20)

Goodbye slideshare UPDATE
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Goodbye slideshare UPDATE
 
Goodbye slideshare
Goodbye slideshareGoodbye slideshare
Goodbye slideshare
 
12 x1 t02 02 integrating exponentials (2014)
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11 x1 t01 03 factorising (2014)
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11 x1 t01 03 factorising (2014)
 
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11 x1 t01 02 binomial products (2014)11 x1 t01 02 binomial products (2014)
11 x1 t01 02 binomial products (2014)
 
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12 x1 t02 01 differentiating exponentials (2014)12 x1 t02 01 differentiating exponentials (2014)
12 x1 t02 01 differentiating exponentials (2014)
 
11 x1 t01 01 algebra & indices (2014)
11 x1 t01 01 algebra & indices (2014)11 x1 t01 01 algebra & indices (2014)
11 x1 t01 01 algebra & indices (2014)
 
12 x1 t01 03 integrating derivative on function (2013)
12 x1 t01 03 integrating derivative on function (2013)12 x1 t01 03 integrating derivative on function (2013)
12 x1 t01 03 integrating derivative on function (2013)
 
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12 x1 t01 02 differentiating logs (2013)
 
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11 x1 t16 07 approximations (2013)
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11 x1 t16 07 approximations (2013)
 
11 x1 t16 06 derivative times function (2013)
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11 x1 t16 06 derivative times function (2013)
 
11 x1 t16 05 volumes (2013)
11 x1 t16 05 volumes (2013)11 x1 t16 05 volumes (2013)
11 x1 t16 05 volumes (2013)
 
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11 x1 t16 03 indefinite integral (2013)11 x1 t16 03 indefinite integral (2013)
11 x1 t16 03 indefinite integral (2013)
 
11 x1 t16 02 definite integral (2013)
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11 x1 t10 02 quadratics and other methods (2013)

  • 2. Quadratics and Completing the Square e.g. 2 Sketch the parabola 8 12y x x  
  • 3. Quadratics and Completing the Square e.g. 2 Sketch the parabola 8 12y x x   2 8 12y x x  
  • 4. Quadratics and Completing the Square e.g. 2 Sketch the parabola 8 12y x x   2 8 12y x x     2 4 4x  
  • 5. Quadratics and Completing the Square e.g. 2 Sketch the parabola 8 12y x x   2 8 12y x x     2 4 4x    vertex is 4, 4  
  • 6. Quadratics and Completing the Square e.g. 2 Sketch the parabola 8 12y x x   2 8 12y x x     2 4 4x    vertex is 4, 4   x intercepts
  • 7. Quadratics and Completing the Square e.g. 2 Sketch the parabola 8 12y x x   2 8 12y x x     2 4 4x    vertex is 4, 4   x intercepts   2 4 4 0x   
  • 8. Quadratics and Completing the Square e.g. 2 Sketch the parabola 8 12y x x   2 8 12y x x     2 4 4x    vertex is 4, 4   x intercepts   2 4 4 0x      2 4 4x  
  • 9. Quadratics and Completing the Square e.g. 2 Sketch the parabola 8 12y x x   2 8 12y x x     2 4 4x    vertex is 4, 4   x intercepts   2 4 4 0x      2 4 4x   4 2 4 2 x x      
  • 10. Quadratics and Completing the Square e.g. 2 Sketch the parabola 8 12y x x   2 8 12y x x     2 4 4x    vertex is 4, 4   x intercepts   2 4 4 0x      2 4 4x   6 or 2x x    4 2 4 2 x x      
  • 11. Quadratics and Completing the Square e.g. 2 Sketch the parabola 8 12y x x   2 8 12y x x     2 4 4x    vertex is 4, 4   x intercepts   2 4 4 0x      2 4 4x   6 or 2x x        intercepts are 6,0 and 2,0 x   4 2 4 2 x x      
  • 12. Quadratics and Completing the Square e.g. 2 Sketch the parabola 8 12y x x   2 8 12y x x     2 4 4x    vertex is 4, 4   x intercepts   2 4 4 0x      2 4 4x   6 or 2x x        intercepts are 6,0 and 2,0 x   4 2 4 2 x x       (ii) Write down the quadratic with roots 2 and 8 and vertex (5,3)
  • 13. Quadratics and Completing the Square e.g. 2 Sketch the parabola 8 12y x x   2 8 12y x x     2 4 4x    vertex is 4, 4   x intercepts   2 4 4 0x      2 4 4x   6 or 2x x        intercepts are 6,0 and 2,0 x   4 2 4 2 x x       (ii) Write down the quadratic with roots 2 and 8 and vertex (5,3)   2 5 3y k x  
  • 14. Quadratics and Completing the Square e.g. 2 Sketch the parabola 8 12y x x   2 8 12y x x     2 4 4x    vertex is 4, 4   x intercepts   2 4 4 0x      2 4 4x   6 or 2x x        intercepts are 6,0 and 2,0 x   4 2 4 2 x x       (ii) Write down the quadratic with roots 2 and 8 and vertex (5,3)   2 5 3y k x       2 2,0 : 0 2 5 3k  
  • 15. Quadratics and Completing the Square e.g. 2 Sketch the parabola 8 12y x x   2 8 12y x x     2 4 4x    vertex is 4, 4   x intercepts   2 4 4 0x      2 4 4x   6 or 2x x        intercepts are 6,0 and 2,0 x   4 2 4 2 x x       (ii) Write down the quadratic with roots 2 and 8 and vertex (5,3)   2 5 3y k x       2 2,0 : 0 2 5 3k   9 3 1 3 k k    
  • 16. Quadratics and Completing the Square e.g. 2 Sketch the parabola 8 12y x x   2 8 12y x x     2 4 4x    vertex is 4, 4   x intercepts   2 4 4 0x      2 4 4x   6 or 2x x        intercepts are 6,0 and 2,0 x   4 2 4 2 x x       (ii) Write down the quadratic with roots 2 and 8 and vertex (5,3)   2 5 3y k x       2 2,0 : 0 2 5 3k   9 3 1 3 k k       21 5 3 3 y x   
  • 17. Quadratics and Completing the Square e.g. 2 Sketch the parabola 8 12y x x   2 8 12y x x     2 4 4x    vertex is 4, 4   x intercepts   2 4 4 0x      2 4 4x   6 or 2x x        intercepts are 6,0 and 2,0 x   4 2 4 2 x x       (ii) Write down the quadratic with roots 2 and 8 and vertex (5,3)   2 5 3y k x       2 2,0 : 0 2 5 3k   9 3 1 3 k k       21 5 3 3 y x     21 10 16 3 y x x   
  • 18. Quadratics and the Discriminant
  • 19. Quadratics and the Discriminant 2 4b ac  
  • 20. Quadratics and the Discriminant 2 4b ac   vertex , 2 4 b a a       
  • 21. Quadratics and the Discriminant 2 4b ac   vertex , 2 4 b a a        zeroes 2 b a    
  • 22. Quadratics and the Discriminant 2 4b ac   vertex , 2 4 b a a        zeroes 2 b a     Note: if 0, no interceptsx 
  • 23. Quadratics and the Discriminant 2 4b ac   vertex , 2 4 b a a        zeroes 2 b a     Note: if 0, no interceptsx  0, one interceptx 
  • 24. Quadratics and the Discriminant 2 4b ac   vertex , 2 4 b a a        zeroes 2 b a     Note: if 0, no interceptsx  0, one interceptx  0, two interceptsx 
  • 25. Quadratics and the Discriminant 2 4b ac   vertex , 2 4 b a a        zeroes 2 b a     Note: if 0, no interceptsx  0, one interceptx  0, two interceptsx  2 e.g. Sketch the parabola 8 12y x x  
  • 26. Quadratics and the Discriminant 2 4b ac   vertex , 2 4 b a a        zeroes 2 b a     Note: if 0, no interceptsx  0, one interceptx  0, two interceptsx    2 8 4 1 12 16     2 e.g. Sketch the parabola 8 12y x x  
  • 27. Quadratics and the Discriminant 2 4b ac   vertex , 2 4 b a a        zeroes 2 b a     Note: if 0, no interceptsx  0, one interceptx  0, two interceptsx    2 8 4 1 12 16     2 e.g. Sketch the parabola 8 12y x x   8 16 vertex , 2 4        
  • 28. Quadratics and the Discriminant 2 4b ac   vertex , 2 4 b a a        zeroes 2 b a     Note: if 0, no interceptsx  0, one interceptx  0, two interceptsx    2 8 4 1 12 16     2 e.g. Sketch the parabola 8 12y x x   8 16 vertex , 2 4          4, 4  
  • 29. Quadratics and the Discriminant 2 4b ac   vertex , 2 4 b a a        zeroes 2 b a     Note: if 0, no interceptsx  0, one interceptx  0, two interceptsx    2 8 4 1 12 16     2 e.g. Sketch the parabola 8 12y x x   8 16 vertex , 2 4          4, 4   Exercise 8B; 1cfi, 2bd, 3c, 4b, 6bei, 10b, 11d, 16, 17, 20* Exercise 8C; 1adg, 2adg, 3ad, 5ac, 8ac, 10, 13*