Quadratics and Completing theSquare
Quadratics and Completing theSquaree.g. 2Sketch the parabola 8 12y x x  
Quadratics and Completing theSquaree.g. 2Sketch the parabola 8 12y x x  28 12y x x  
Quadratics and Completing theSquaree.g. 2Sketch the parabola 8 12y x x  28 12y x x   24 4x  
Quadratics and Completing theSquaree.g. 2Sketch the parabola 8 12y x x  28 12y x x   24 4x   vertex is 4, 4 ...
Quadratics and Completing theSquaree.g. 2Sketch the parabola 8 12y x x  28 12y x x   24 4x   vertex is 4, 4 ...
Quadratics and Completing theSquaree.g. 2Sketch the parabola 8 12y x x  28 12y x x   24 4x   vertex is 4, 4 ...
Quadratics and Completing theSquaree.g. 2Sketch the parabola 8 12y x x  28 12y x x   24 4x   vertex is 4, 4 ...
Quadratics and Completing theSquaree.g. 2Sketch the parabola 8 12y x x  28 12y x x   24 4x   vertex is 4, 4 ...
Quadratics and Completing theSquaree.g. 2Sketch the parabola 8 12y x x  28 12y x x   24 4x   vertex is 4, 4 ...
Quadratics and Completing theSquaree.g. 2Sketch the parabola 8 12y x x  28 12y x x   24 4x   vertex is 4, 4 ...
Quadratics and Completing theSquaree.g. 2Sketch the parabola 8 12y x x  28 12y x x   24 4x   vertex is 4, 4 ...
Quadratics and Completing theSquaree.g. 2Sketch the parabola 8 12y x x  28 12y x x   24 4x   vertex is 4, 4 ...
Quadratics and Completing theSquaree.g. 2Sketch the parabola 8 12y x x  28 12y x x   24 4x   vertex is 4, 4 ...
Quadratics and Completing theSquaree.g. 2Sketch the parabola 8 12y x x  28 12y x x   24 4x   vertex is 4, 4 ...
Quadratics and Completing theSquaree.g. 2Sketch the parabola 8 12y x x  28 12y x x   24 4x   vertex is 4, 4 ...
Quadratics and Completing theSquaree.g. 2Sketch the parabola 8 12y x x  28 12y x x   24 4x   vertex is 4, 4 ...
Quadratics and the Discriminant
Quadratics and the Discriminant24b ac  
Quadratics and the Discriminant24b ac  vertex ,2 4ba a     
Quadratics and the Discriminant24b ac  vertex ,2 4ba a     zeroes2ba  
Quadratics and the Discriminant24b ac  vertex ,2 4ba a     zeroes2ba  Note: if 0, no interceptsx 
Quadratics and the Discriminant24b ac  vertex ,2 4ba a     zeroes2ba  Note: if 0, no interceptsx 0, one...
Quadratics and the Discriminant24b ac  vertex ,2 4ba a     zeroes2ba  Note: if 0, no interceptsx 0, one...
Quadratics and the Discriminant24b ac  vertex ,2 4ba a     zeroes2ba  Note: if 0, no interceptsx 0, one...
Quadratics and the Discriminant24b ac  vertex ,2 4ba a     zeroes2ba  Note: if 0, no interceptsx 0, one...
Quadratics and the Discriminant24b ac  vertex ,2 4ba a     zeroes2ba  Note: if 0, no interceptsx 0, one...
Quadratics and the Discriminant24b ac  vertex ,2 4ba a     zeroes2ba  Note: if 0, no interceptsx 0, one...
Quadratics and the Discriminant24b ac  vertex ,2 4ba a     zeroes2ba  Note: if 0, no interceptsx 0, one...
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11 x1 t10 02 quadratics and other methods (2013)

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11 x1 t10 02 quadratics and other methods (2013)

  1. 1. Quadratics and Completing theSquare
  2. 2. Quadratics and Completing theSquaree.g. 2Sketch the parabola 8 12y x x  
  3. 3. Quadratics and Completing theSquaree.g. 2Sketch the parabola 8 12y x x  28 12y x x  
  4. 4. Quadratics and Completing theSquaree.g. 2Sketch the parabola 8 12y x x  28 12y x x   24 4x  
  5. 5. Quadratics and Completing theSquaree.g. 2Sketch the parabola 8 12y x x  28 12y x x   24 4x   vertex is 4, 4  
  6. 6. Quadratics and Completing theSquaree.g. 2Sketch the parabola 8 12y x x  28 12y x x   24 4x   vertex is 4, 4  x intercepts
  7. 7. Quadratics and Completing theSquaree.g. 2Sketch the parabola 8 12y x x  28 12y x x   24 4x   vertex is 4, 4  x intercepts  24 4 0x   
  8. 8. Quadratics and Completing theSquaree.g. 2Sketch the parabola 8 12y x x  28 12y x x   24 4x   vertex is 4, 4  x intercepts  24 4 0x    24 4x  
  9. 9. Quadratics and Completing theSquaree.g. 2Sketch the parabola 8 12y x x  28 12y x x   24 4x   vertex is 4, 4  x intercepts  24 4 0x    24 4x  4 24 2xx    
  10. 10. Quadratics and Completing theSquaree.g. 2Sketch the parabola 8 12y x x  28 12y x x   24 4x   vertex is 4, 4  x intercepts  24 4 0x    24 4x  6 or 2x x   4 24 2xx    
  11. 11. Quadratics and Completing theSquaree.g. 2Sketch the parabola 8 12y x x  28 12y x x   24 4x   vertex is 4, 4  x intercepts  24 4 0x    24 4x  6 or 2x x      intercepts are6,0 and 2,0x 4 24 2xx    
  12. 12. Quadratics and Completing theSquaree.g. 2Sketch the parabola 8 12y x x  28 12y x x   24 4x   vertex is 4, 4  x intercepts  24 4 0x    24 4x  6 or 2x x      intercepts are6,0 and 2,0x 4 24 2xx    (ii) Write down the quadratic with roots 2 and 8 and vertex (5,3)
  13. 13. Quadratics and Completing theSquaree.g. 2Sketch the parabola 8 12y x x  28 12y x x   24 4x   vertex is 4, 4  x intercepts  24 4 0x    24 4x  6 or 2x x      intercepts are6,0 and 2,0x 4 24 2xx    (ii) Write down the quadratic with roots 2 and 8 and vertex (5,3)  25 3y k x  
  14. 14. Quadratics and Completing theSquaree.g. 2Sketch the parabola 8 12y x x  28 12y x x   24 4x   vertex is 4, 4  x intercepts  24 4 0x    24 4x  6 or 2x x      intercepts are6,0 and 2,0x 4 24 2xx    (ii) Write down the quadratic with roots 2 and 8 and vertex (5,3)  25 3y k x      22,0 : 0 2 5 3k  
  15. 15. Quadratics and Completing theSquaree.g. 2Sketch the parabola 8 12y x x  28 12y x x   24 4x   vertex is 4, 4  x intercepts  24 4 0x    24 4x  6 or 2x x      intercepts are6,0 and 2,0x 4 24 2xx    (ii) Write down the quadratic with roots 2 and 8 and vertex (5,3)  25 3y k x      22,0 : 0 2 5 3k  9 313kk  
  16. 16. Quadratics and Completing theSquaree.g. 2Sketch the parabola 8 12y x x  28 12y x x   24 4x   vertex is 4, 4  x intercepts  24 4 0x    24 4x  6 or 2x x      intercepts are6,0 and 2,0x 4 24 2xx    (ii) Write down the quadratic with roots 2 and 8 and vertex (5,3)  25 3y k x      22,0 : 0 2 5 3k  9 313kk    215 33y x   
  17. 17. Quadratics and Completing theSquaree.g. 2Sketch the parabola 8 12y x x  28 12y x x   24 4x   vertex is 4, 4  x intercepts  24 4 0x    24 4x  6 or 2x x      intercepts are6,0 and 2,0x 4 24 2xx    (ii) Write down the quadratic with roots 2 and 8 and vertex (5,3)  25 3y k x      22,0 : 0 2 5 3k  9 313kk    215 33y x    2110 163y x x   
  18. 18. Quadratics and the Discriminant
  19. 19. Quadratics and the Discriminant24b ac  
  20. 20. Quadratics and the Discriminant24b ac  vertex ,2 4ba a     
  21. 21. Quadratics and the Discriminant24b ac  vertex ,2 4ba a     zeroes2ba  
  22. 22. Quadratics and the Discriminant24b ac  vertex ,2 4ba a     zeroes2ba  Note: if 0, no interceptsx 
  23. 23. Quadratics and the Discriminant24b ac  vertex ,2 4ba a     zeroes2ba  Note: if 0, no interceptsx 0, one interceptx 
  24. 24. Quadratics and the Discriminant24b ac  vertex ,2 4ba a     zeroes2ba  Note: if 0, no interceptsx 0, one interceptx 0, two interceptsx 
  25. 25. Quadratics and the Discriminant24b ac  vertex ,2 4ba a     zeroes2ba  Note: if 0, no interceptsx 0, one interceptx 0, two interceptsx 2e.g. Sketch the parabola 8 12y x x  
  26. 26. Quadratics and the Discriminant24b ac  vertex ,2 4ba a     zeroes2ba  Note: if 0, no interceptsx 0, one interceptx 0, two interceptsx   28 4 1 1216  2e.g. Sketch the parabola 8 12y x x  
  27. 27. Quadratics and the Discriminant24b ac  vertex ,2 4ba a     zeroes2ba  Note: if 0, no interceptsx 0, one interceptx 0, two interceptsx   28 4 1 1216  2e.g. Sketch the parabola 8 12y x x  8 16vertex ,2 4      
  28. 28. Quadratics and the Discriminant24b ac  vertex ,2 4ba a     zeroes2ba  Note: if 0, no interceptsx 0, one interceptx 0, two interceptsx   28 4 1 1216  2e.g. Sketch the parabola 8 12y x x  8 16vertex ,2 4       4, 4  
  29. 29. Quadratics and the Discriminant24b ac  vertex ,2 4ba a     zeroes2ba  Note: if 0, no interceptsx 0, one interceptx 0, two interceptsx   28 4 1 1216  2e.g. Sketch the parabola 8 12y x x  8 16vertex ,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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