11x1 t11 02 quadratics and other methods

Quadratics and Completing the Square

Quadratics and Completing the Square

e.g. 2Sketch the parabola 8 12y x x

Quadratics and Completing the Square

e.g. 2Sketch the parabola 8 12y x x 2 8 12y x x

Quadratics and Completing the Square

e.g. 2Sketch the parabola 8 12y x x 2 8 12y x x

24 4x

Quadratics and Completing the Square

e.g. 2Sketch the parabola 8 12y x x 2 8 12y x x

24 4x

vertex is 4, 4

Quadratics and Completing the Square

e.g. 2Sketch the parabola 8 12y x x 2 8 12y x x

24 4x

vertex is 4, 4

x intercepts

Quadratics and Completing the Square

e.g. 2Sketch the parabola 8 12y x x 2 8 12y x x

24 4x

vertex is 4, 4

x intercepts 24 4 0x

Quadratics and Completing the Square

e.g. 2Sketch the parabola 8 12y x x 2 8 12y x x

24 4x

vertex is 4, 4

x intercepts 24 4 0x

24 4x

Quadratics and Completing the Square

e.g. 2Sketch the parabola 8 12y x x 2 8 12y x x

24 4x

vertex is 4, 4

x intercepts 24 4 0x

24 4x 4 2

4 2x

x

Quadratics and Completing the Square

e.g. 2Sketch the parabola 8 12y x x 2 8 12y x x

24 4x

vertex is 4, 4

x intercepts 24 4 0x

24 4x

6 or 2x x

4 24 2

xx

Quadratics and Completing the Square

e.g. 2Sketch the parabola 8 12y x x 2 8 12y x x

24 4x

vertex is 4, 4

x intercepts 24 4 0x

24 4x

6 or 2x x

intercepts are

6,0 and 2,0x

4 24 2

xx

Quadratics and Completing the Square

e.g. 2Sketch the parabola 8 12y x x 2 8 12y x x

24 4x

vertex is 4, 4

x intercepts 24 4 0x

24 4x

6 or 2x x

intercepts are

6,0 and 2,0x

4 24 2

xx

(ii) Write down the quadratic with roots 2 and 8 and vertex (5,3)

Quadratics and Completing the Square

e.g. 2Sketch the parabola 8 12y x x 2 8 12y x x

24 4x

vertex is 4, 4

x intercepts 24 4 0x

24 4x

6 or 2x x

intercepts are

6,0 and 2,0x

4 24 2

xx

(ii) Write down the quadratic with roots 2 and 8 and vertex (5,3) 25 3y k x

Quadratics and Completing the Square

e.g. 2Sketch the parabola 8 12y x x 2 8 12y x x

24 4x

vertex is 4, 4

x intercepts 24 4 0x

24 4x

6 or 2x x

intercepts are

6,0 and 2,0x

4 24 2

xx

(ii) Write down the quadratic with roots 2 and 8 and vertex (5,3) 25 3y k x

22,0 : 0 2 5 3k

Quadratics and Completing the Square

e.g. 2Sketch the parabola 8 12y x x 2 8 12y x x

24 4x

vertex is 4, 4

x intercepts 24 4 0x

24 4x

6 or 2x x

intercepts are

6,0 and 2,0x

4 24 2

xx

(ii) Write down the quadratic with roots 2 and 8 and vertex (5,3) 25 3y k x

22,0 : 0 2 5 3k

9 313

k

k

Quadratics and Completing the Square

e.g. 2Sketch the parabola 8 12y x x 2 8 12y x x

24 4x

vertex is 4, 4

x intercepts 24 4 0x

24 4x

6 or 2x x

intercepts are

6,0 and 2,0x

4 24 2

xx

(ii) Write down the quadratic with roots 2 and 8 and vertex (5,3) 25 3y k x

22,0 : 0 2 5 3k

9 313

k

k

21 5 33

y x

Quadratics and Completing the Square

e.g. 2Sketch the parabola 8 12y x x 2 8 12y x x

24 4x

vertex is 4, 4

x intercepts 24 4 0x

24 4x

6 or 2x x

intercepts are

6,0 and 2,0x

4 24 2

xx

(ii) Write down the quadratic with roots 2 and 8 and vertex (5,3) 25 3y k x

22,0 : 0 2 5 3k

9 313

k

k

21 5 33

y x

21 10 163

y x x

Quadratics and the Discriminant

Quadratics and the Discriminant2 4b ac

Quadratics and the Discriminant2 4b ac

vertex ,2 4ba a

Quadratics and the Discriminant2 4b ac

vertex ,2 4ba a

zeroes2

ba

Quadratics and the Discriminant2 4b ac

vertex ,2 4ba a

zeroes2

ba

Note: if 0, no interceptsx

Quadratics and the Discriminant2 4b ac

vertex ,2 4ba a

zeroes2

ba

Note: if 0, no interceptsx 0, one interceptx

Quadratics and the Discriminant2 4b ac

vertex ,2 4ba a

zeroes2

ba

Note: if 0, no interceptsx 0, one interceptx 0, two interceptsx

Quadratics and the Discriminant2 4b ac

vertex ,2 4ba a

zeroes2

ba

Note: if 0, no interceptsx 0, one interceptx 0, two interceptsx

2e.g. Sketch the parabola 8 12y x x

Quadratics and the Discriminant2 4b ac

vertex ,2 4ba a

zeroes2

ba

Note: if 0, no interceptsx 0, one interceptx 0, two interceptsx

28 4 1 1216

2e.g. Sketch the parabola 8 12y x x

Quadratics and the Discriminant2 4b ac

vertex ,2 4ba a

zeroes2

ba

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 16 vertex ,2 4

Quadratics and the Discriminant2 4b ac

vertex ,2 4ba a

zeroes2

ba

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 16 vertex ,2 4

4, 4

Quadratics and the Discriminant2 4b ac

vertex ,2 4ba a

zeroes2

ba

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 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*