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Quadratics of the Form
y = a(x – h)2 + k
stretch/compressionreflection
H. Shift left/right
V. Shift up/down
![Page 2: Quadratics of the Form y = a(x – h) 2 + k stretch/compression reflection H. Shift left/right V. Shift up/down](https://reader035.vdocuments.net/reader035/viewer/2022062317/5a4d1b2f7f8b9ab05999a973/html5/thumbnails/2.jpg)
y = x2Opening: up/downStretch: none/ stretched/ compressed
Vertex: (0, 0)
Horizontal shift
Vertical shift
1)
2)
3)
4)
5)
none
none
![Page 3: Quadratics of the Form y = a(x – h) 2 + k stretch/compression reflection H. Shift left/right V. Shift up/down](https://reader035.vdocuments.net/reader035/viewer/2022062317/5a4d1b2f7f8b9ab05999a973/html5/thumbnails/3.jpg)
Equation open stretch shrink left/right up/down vertex
1 y = 2x2
2 y = x2 – 5
3 y = (x + 4)2
4 y = – x2 + 5
5 y = x2 + 3
6 y = (x – 3)2
up
up
up
down
up
up
stretch
normal
normal
normal
normal
normal
left 4
right 3
down 5
up 5
up 3
(0,0)
(0, –5)
(–4,0)
(0,5)
(0,3)
(3,0)
no
no
no
no
no
no
no
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Equation open stretch shrink left/right up/down vertex
7
8 y = –3(x + 2)2
9 y = (x + 3)2 – 4
10
11 y = (x – 2)2 – 4
12
down
down
up
up
up
down
shrink
stretch
normal
shrink
normal
shrink
left 3
right 3
no
down 5
down 4
(–2,0)
(–2,0)
(–3,–4)
(1, –5)
(2, –4)
(3,6)
left 2
left 2
right 1
right 2
no
down 4
up 6
21 ( 2)2
y x
21 ( 1) 54
y x
21 ( 3) 62
y x
![Page 5: Quadratics of the Form y = a(x – h) 2 + k stretch/compression reflection H. Shift left/right V. Shift up/down](https://reader035.vdocuments.net/reader035/viewer/2022062317/5a4d1b2f7f8b9ab05999a973/html5/thumbnails/5.jpg)
y = 2x2Opening: up/downStretch: none/ stretched/ compressed
Vertex: (0, 0)
Horizontal Shift
Vertical Shift
1)
2)
3)
4)
5)
none
none
(1)
![Page 6: Quadratics of the Form y = a(x – h) 2 + k stretch/compression reflection H. Shift left/right V. Shift up/down](https://reader035.vdocuments.net/reader035/viewer/2022062317/5a4d1b2f7f8b9ab05999a973/html5/thumbnails/6.jpg)
y = x2 – 5Opening: up/downStretch: none / stretched/ shrunk
Vertex: (0, –5)
Horizontal Shift
Vertical Shift
1)
2)
3)
4)
5)
none
down 5
(2)
![Page 7: Quadratics of the Form y = a(x – h) 2 + k stretch/compression reflection H. Shift left/right V. Shift up/down](https://reader035.vdocuments.net/reader035/viewer/2022062317/5a4d1b2f7f8b9ab05999a973/html5/thumbnails/7.jpg)
y = (x + 4)2Opening: up/downStretch: none / stretched/ compressed
Vertex: (– 4, 0)
Horizontal shift
Vertical shift
1)
2)
3)
4)
5)
left 4 or (-4)
none
(3)
![Page 8: Quadratics of the Form y = a(x – h) 2 + k stretch/compression reflection H. Shift left/right V. Shift up/down](https://reader035.vdocuments.net/reader035/viewer/2022062317/5a4d1b2f7f8b9ab05999a973/html5/thumbnails/8.jpg)
y = – x2 + 5Opening: up/downStretch: none/ stretched/ compressed
Vertex: (0, 5)
Horizontal shift
Vertical shift
1)
2)
3)
4)
5)
none
up 5 or (+5)
(4)
![Page 9: Quadratics of the Form y = a(x – h) 2 + k stretch/compression reflection H. Shift left/right V. Shift up/down](https://reader035.vdocuments.net/reader035/viewer/2022062317/5a4d1b2f7f8b9ab05999a973/html5/thumbnails/9.jpg)
y = x2 + 3Opening: up/downStretch: NONE/ stretched/ compressed
Vertex: (0, 3)
Horizontal shift
Vertical shift
1)
2)
3)
4)
5)
none
up 3 or (+3)
(5)
![Page 10: Quadratics of the Form y = a(x – h) 2 + k stretch/compression reflection H. Shift left/right V. Shift up/down](https://reader035.vdocuments.net/reader035/viewer/2022062317/5a4d1b2f7f8b9ab05999a973/html5/thumbnails/10.jpg)
y = (x – 3)2Opening: up/downStretch: NONE/ stretched/ compressed
Vertex: (3, 0)
Horizontal shift
Vertical shift
1)
2)
3)
4)
5)
right 3 or (+3)
none
(6)
![Page 11: Quadratics of the Form y = a(x – h) 2 + k stretch/compression reflection H. Shift left/right V. Shift up/down](https://reader035.vdocuments.net/reader035/viewer/2022062317/5a4d1b2f7f8b9ab05999a973/html5/thumbnails/11.jpg)
Opening: up/downStretch: NONE/ stretched/ compressed
Vertex: (–2, 0)
Horizontal shift
Vertical shift
1)
2)
3)
4)
5)
left 2 or (-2)
none
21 ( 2)2
y x
(7)
![Page 12: Quadratics of the Form y = a(x – h) 2 + k stretch/compression reflection H. Shift left/right V. Shift up/down](https://reader035.vdocuments.net/reader035/viewer/2022062317/5a4d1b2f7f8b9ab05999a973/html5/thumbnails/12.jpg)
y = –3(x + 2)2Opening: up/downStretch: NONE/ stretched/ compressed
Vertex: (–2, 0)
Horizontal shift
Vertical shift
1)
2)
3)
4)
5)
left 2 or (-2)
none
(8)
![Page 13: Quadratics of the Form y = a(x – h) 2 + k stretch/compression reflection H. Shift left/right V. Shift up/down](https://reader035.vdocuments.net/reader035/viewer/2022062317/5a4d1b2f7f8b9ab05999a973/html5/thumbnails/13.jpg)
y = (x + 3)2 – 4Opening: up/downStretch: NONE/ stretched/ compressed
Vertex: (– 3,– 4)
Horizontal shift
Vertical shift
1)
2)
3)
4)
5)
left 3 or (-3)
down 4 or (-4)
(9)
![Page 14: Quadratics of the Form y = a(x – h) 2 + k stretch/compression reflection H. Shift left/right V. Shift up/down](https://reader035.vdocuments.net/reader035/viewer/2022062317/5a4d1b2f7f8b9ab05999a973/html5/thumbnails/14.jpg)
Opening: up/downStretch: NONE/ stretched/ compressed
Vertex: (1, – 5)
Horizontal shift
Vertical shift
1)
2)
3)
4)
5)
right 1 or (+1)
down 5 or (-5)
21 ( 1) 54
y x
(10)
![Page 15: Quadratics of the Form y = a(x – h) 2 + k stretch/compression reflection H. Shift left/right V. Shift up/down](https://reader035.vdocuments.net/reader035/viewer/2022062317/5a4d1b2f7f8b9ab05999a973/html5/thumbnails/15.jpg)
y = (x – 2)2 – 4Opening: up/downStretch: NONE/ stretched/ compressed
Vertex: (2, – 4)
Horizontal shift
Vertical shift
1)
2)
3)
4)
5)
right 2 or (+2)
down 4 or (-4)
(11)
![Page 16: Quadratics of the Form y = a(x – h) 2 + k stretch/compression reflection H. Shift left/right V. Shift up/down](https://reader035.vdocuments.net/reader035/viewer/2022062317/5a4d1b2f7f8b9ab05999a973/html5/thumbnails/16.jpg)
Opening: up/downStretch: NONE/ stretched/ compressed
Vertex: (3, 6)
Horizontal shift
Vertical shift
1)
2)
3)
4)
5)
right 3 or (+3)
up 6 or (+6)
21 ( 3) 62
y x
(12)