Transformations in Vertex Form

shifted up 8 units

shifted down 8 units

shifted left 8 units

shifted right 8 units

Shifted down 4 units

Shifted left 4 units

Shifted right 4 units

Shifted up 4 units

translated left 9, up 5

translated left 9, down 5

translated right 9, up 5

translated right 9, down 5

translated left 7

translated right 7

translated up 7

translated down 7

translated right 5, up 1

translated left 5, down 1

translated right 5, down 1

translated left 5, up 1

Compress by 2, shifted 2 units left and 5 down

Stretch by 5, shifted 5 units left and 2 down

Stretch by 2, shifted 2 units left and 5 down

Compress by 5, shifted 2 units left and 2 down

Compress by 2, shifted 2 units left and 5 down

Stretch by 5, shifted 5 units left and 2 down

Stretch by 2, shifted 2 units left and 5 down

Compress by 5, shifted 2 units left and 2 down

shrink

stretch

reflection, stretch

reflection, shrink

shrink, left 4, down 5

stretch, left 4, down 5

reflection, left 4, down 5

reflection, shrink, left 4, down 5

Vertical compression (wider)

Vertical stretch (narrower)

Vertical compression (wider) and reflection over x-axis

Vertical stretch (narrower) and reflection over x-axis

reflect over the x-axis

reflect over the x-axis, left: 3, up: 6

stretch, left: 3, down: 6

left: 3, down: 6

left: 1, up: 4

left: 1, down: 4

right: 1, up: 4

right: 4, up: 1

a=2, h=-4, k=-1

a=-2, h=4, k=1

a=2, h=4, k=1

a=-2, h=-4, k=1

a=-1, h=3, k=2

a=3, h=3, k=3

a=1, h=-3, k=2

a=1, h=-3, k=-2

Narrow

Wider

$$y=\left(x+3\right)^2+4$$  

$$y=\left(x+4\right)^2+3$$  

$$y=\left(x+4\right)^2-3$$  

$$y=\left(x+3\right)^2-4$$  

right 3, down 2

up 3, left 2

left 3, up 2

left 3, down 2

$$f\left(x\right)=\frac{1}{2}x^2$$

$$f\left(x\right)=x^2$$

$$f\left(x\right)=3x^2$$

$$f\left(x\right)=5x^2$$

Horizontal shift left 6, vertical shift up 2

Horizontal shift left 6, vertical shift down 2

Horizontal shift right 6, vertical shift down 2

Horizontal shift right 6, vertical shift up 2

vertical reflection and vertical shift down

vertical reflection and vertical stretch

horizontal stretch

vertical reflection and vertical compression

becoming wider or vertically compressed

becoming narrower or vertically stretched