Transformations of Parent Functions

Translated left 2 units

Reflected over x-axis

Vertically stretched and reflected over x-axis

Compressed vertically and reflected over the x-axis

Reflect over x, right 3, down 4

Reflect over y, right 3, down 4

Reflect over x, right 3, up 4

Reflect over y, left 3, down 4

Vertical Stretch of 5

Down 2

Vertical Compression of 5

Up 2

Vertical Stretch of 5

Up 2

Vertical Compression of 5

Down 2

vertical stretch by 1/2, left 1, down 3

horizontal stretch by 1/2, right 1, down 3

vertical compression by 1/2, left 1, down 3

horizontal compression by 1/2, right 1, down 3

reflect over y, vertical compression by 2, right 5, up 1

reflect over x, horizontal compression by 2, left 5, up 1

reflect over x, vertical stretch by 2, right 5, up 1

reflect over y, horizontal stretch by -2, right 5, up 1

Horizontal translation left

Vertical compression

Vertical translation down

Horizontal translation right

Vertical stretch

 $f\left(x\right)=4\left(x+2\right)^2+3$  

 $f\left(x\right)=4\left(x-2\right)^2+3$  

 $f\left(x\right)=3\left(x+2\right)^2+4$  

 $f\left(x\right)=2\left(x-4\right)^2+3$  

Vertical stretch

Vertical compression

Vertical translation up

Reflection over the x-axis

No Transformation

Vertical stretch

Vertical compression

Vertical translation down

Reflection over the x-axis

No transformation

Vertically Stretches by 3, Shifts left 8

Vertically Stretches by 3, Shifts right 8

Vertically Stretches by 3, Shifts up 8

Vertically Stretches by 3, Shifts down 8