11X1 T11 02 quadratics and other methods
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11X1 T11 02 quadratics and other methods 11X1 T11 02 quadratics and other methods Presentation Transcript

  • Quadratics and Completing the Square
  • Quadratics and Completing the Square e.g. Sketch the parabola y  x 2  8 x  12
  • Quadratics and Completing the Square e.g. Sketch the parabola y  x 2  8 x  12 y  x 2  8 x  12
  • 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
  • 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 
  • 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 
  • 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 
  • 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 
  • 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
  • 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
  • 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 
  • 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)
  • 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
  • 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
  • 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
  • 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
  • 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
  • Quadratics and the Discriminant
  • Quadratics and the Discriminant   b 2  4ac
  • Quadratics and the Discriminant   b 2  4ac b  vertex   ,     2a 4a 
  • Quadratics and the Discriminant   b 2  4ac b  vertex   ,     2a 4a  b   zeroes  2a
  • Quadratics and the Discriminant   b 2  4ac b  vertex   ,    Note: if   0, no x intercepts  2a 4a  b   zeroes  2a
  • Quadratics and the Discriminant   b 2  4ac b  vertex   ,    Note: if   0, no x intercepts  2a 4a    0, one x intercept b   zeroes  2a
  • 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
  • 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
  • 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
  • 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
  • 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 
  • 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*