11X1 T10 02 quadratics and other methods (2010)

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11X1 T10 02 quadratics and other methods (2010)

  1. 1. Quadratics and Completing the Square
  2. 2. Quadratics and Completing the Square e.g. Sketch the parabola y  x 2  8 x  12
  3. 3. Quadratics and Completing the Square e.g. Sketch the parabola y  x 2  8 x  12 y  x 2  8 x  12
  4. 4. Quadratics and Completing the Square e.g. Sketch the parabola y  x 2  8 x  12 y  x 2  8 x  12   x  4  4 2
  5. 5. Quadratics and Completing the Square e.g. Sketch the parabola y  x 2  8 x  12 y  x 2  8 x  12   x  4  4 2  vertex is  4, 4 
  6. 6. Quadratics and Completing the Square e.g. Sketch the parabola y  x 2  8 x  12 y  x 2  8 x  12 x intercepts   x  4  4 2  vertex is  4, 4 
  7. 7. Quadratics and Completing the Square e.g. Sketch the parabola y  x 2  8 x  12  x  4  4  0 2 y  x 2  8 x  12 x intercepts   x  4  4 2  vertex is  4, 4 
  8. 8. Quadratics and Completing the Square e.g. Sketch the parabola y  x 2  8 x  12  x  4  4  0 2 y  x 2  8 x  12 x intercepts  x  4  4 2   x  4  4 2  vertex is  4, 4 
  9. 9. Quadratics and Completing the Square e.g. Sketch the parabola y  x 2  8 x  12  x  4  4  0 2 y  x 2  8 x  12 x intercepts  x  4  4 2   x  4  4 2  vertex is  4, 4  x  4  2 x  4  2
  10. 10. Quadratics and Completing the Square e.g. Sketch the parabola y  x 2  8 x  12  x  4  4  0 2 y  x 2  8 x  12 x intercepts  x  4  4 2   x  4  4 2  vertex is  4, 4  x  4  2 x  4  2 x  6 or x  2
  11. 11. Quadratics and Completing the Square e.g. Sketch the parabola y  x 2  8 x  12  x  4  4  0 2 y  x 2  8 x  12 x intercepts  x  4  4 2   x  4  4 2  vertex is  4, 4  x  4  2 x  4  2 x  6 or x  2  x intercepts are  6,0  and  2,0 
  12. 12. Quadratics and Completing the Square e.g. Sketch the parabola y  x 2  8 x  12  x  4  4  0 2 y  x 2  8 x  12 x intercepts  x  4  4 2   x  4  4 2  vertex is  4, 4  x  4  2 x  4  2 x  6 or x  2  x intercepts are  6,0  and  2,0  (ii) Write down the quadratic with roots 2 and 8 and vertex (5,3)
  13. 13. Quadratics and Completing the Square e.g. Sketch the parabola y  x 2  8 x  12  x  4  4  0 2 y  x 2  8 x  12 x intercepts  x  4  4 2   x  4  4 2  vertex is  4, 4  x  4  2 x  4  2 x  6 or x  2  x intercepts are  6,0  and  2,0  (ii) Write down the quadratic with roots 2 and 8 and vertex (5,3)   y  k  x  5  3 2
  14. 14. Quadratics and Completing the Square e.g. Sketch the parabola y  x 2  8 x  12  x  4  4  0 2 y  x 2  8 x  12 x intercepts  x  4  4 2   x  4  4 2  vertex is  4, 4  x  4  2 x  4  2 x  6 or x  2  x intercepts are  6,0  and  2,0  (ii) Write down the quadratic with roots 2 and 8 and vertex (5,3)   y  k  x  5  3 2  2,0  : 0  k  2  5   3 2
  15. 15. Quadratics and Completing the Square e.g. Sketch the parabola y  x 2  8 x  12  x  4  4  0 2 y  x 2  8 x  12 x intercepts  x  4  4 2   x  4  4 2  vertex is  4, 4  x  4  2 x  4  2 x  6 or x  2  x intercepts are  6,0  and  2,0  (ii) Write down the quadratic with roots 2 and 8 and vertex (5,3)   y  k  x  5  3 2 9k  3  2,0  : 0  k  2  5   3 1 k  2 3
  16. 16. Quadratics and Completing the Square e.g. Sketch the parabola y  x 2  8 x  12  x  4  4  0 2 y  x 2  8 x  12 x intercepts  x  4  4 2   x  4  4 2  vertex is  4, 4  x  4  2 x  4  2 x  6 or x  2  x intercepts are  6,0  and  2,0  (ii) Write down the quadratic with roots 2 and 8 and vertex (5,3)  2  y  k  x  5  3 9k  3 1  y    x  5  3 3 2     2,0  : 0  k  2  5  3 2 k  1 3
  17. 17. Quadratics and Completing the Square e.g. Sketch the parabola y  x 2  8 x  12  x  4  4  0 2 y  x 2  8 x  12 x intercepts  x  4  4 2   x  4  4 2  vertex is  4, 4  x  4  2 x  4  2 x  6 or x  2  x intercepts are  6,0  and  2,0  (ii) Write down the quadratic with roots 2 and 8 and vertex (5,3)  2  y  k  x  5  3 9k  3 1  y    x  5  3 3 2     2,0  : 0  k  2  5  3 2 k  1 3 y    x  10 x  16  1 2 3
  18. 18. Quadratics and the Discriminant
  19. 19. Quadratics and the Discriminant   b 2  4ac
  20. 20. Quadratics and the Discriminant   b 2  4ac b  vertex   ,     2a 4a 
  21. 21. Quadratics and the Discriminant   b 2  4ac b  vertex   ,     2a 4a  b   zeroes  2a
  22. 22. Quadratics and the Discriminant   b 2  4ac b  vertex   ,    Note: if   0, no x intercepts  2a 4a  b   zeroes  2a
  23. 23. Quadratics and the Discriminant   b 2  4ac b  vertex   ,    Note: if   0, no x intercepts  2a 4a    0, one x intercept b   zeroes  2a
  24. 24. Quadratics and the Discriminant   b 2  4ac b  vertex   ,    Note: if   0, no x intercepts  2a 4a    0, one x intercept b     0, two x intercepts zeroes  2a
  25. 25. Quadratics and the Discriminant   b 2  4ac b  vertex   ,    Note: if   0, no x intercepts  2a 4a    0, one x intercept b     0, two x intercepts zeroes  2a e.g. Sketch the parabola y  x 2  8 x  12
  26. 26. Quadratics and the Discriminant   b 2  4ac b  vertex   ,    Note: if   0, no x intercepts  2a 4a    0, one x intercept b     0, two x intercepts zeroes  2a e.g. Sketch the parabola y  x 2  8 x  12   82  4 112   16
  27. 27. Quadratics and the Discriminant   b 2  4ac b  vertex   ,    Note: if   0, no x intercepts  2a 4a    0, one x intercept b     0, two x intercepts zeroes  2a e.g. Sketch the parabola y  x 2  8 x  12   82  4 112   16   8 ,  16   vertex     2 4
  28. 28. Quadratics and the Discriminant   b 2  4ac b  vertex   ,    Note: if   0, no x intercepts  2a 4a    0, one x intercept b     0, two x intercepts zeroes  2a e.g. Sketch the parabola y  x 2  8 x  12   82  4 112   16   8 ,  16   vertex     2 4   4, 4 
  29. 29. Quadratics and the Discriminant   b 2  4ac b  vertex   ,    Note: if   0, no x intercepts  2a 4a    0, one x intercept b     0, two x intercepts zeroes  2a e.g. Sketch the parabola y  x 2  8 x  12   82  4 112   16 Exercise 8B; 1cfi, 2bd, 3c, 4b, 6bei, 10b,   8 ,  16  11d, 16, 17, 20*  vertex     2 4 Exercise 8C; 1adg, 2adg, 3ad, 5ac, 8ac,   4, 4  10, 13*

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