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# 11X1 T11 02 quadratics and other methods

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### 11X1 T11 02 quadratics and other methods

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*