Quadratics of the Form

y = a(x – h)2 + k

stretch/compressionreflection

H. Shift left/right

V. Shift up/down

y = x2Opening: up/downStretch: none/ stretched/ compressed

Vertex: (0, 0)

Horizontal shift

Vertical shift

1)

2)

3)

4)

5)

none

none

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

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

y = 2x2Opening: up/downStretch: none/ stretched/ compressed

Vertex: (0, 0)

Horizontal Shift

Vertical Shift

1)

2)

3)

4)

5)

none

none

(1)

y = x2 – 5Opening: up/downStretch: none / stretched/ shrunk

Vertex: (0, –5)

Horizontal Shift

Vertical Shift

1)

2)

3)

4)

5)

none

down 5

(2)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)