11X1 T10 02 quadratics and other methods (2011)
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Quadratics and Completing the Square
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Transcript of 11X1 T10 02 quadratics and other methods (2011)
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*
