Transformations of Parabolas and Absolute

It has a horizontal translation of right 2

It has a horizontal translation of left 2

It has a vertical translation of up 1

It has a vertical translation of down 1

vertical reflection

vertical translation

dilation

rotation

horizontal reflection

Horizontal Translation

Vertical Translation

Dilation:

Stretch

Vertical Reflection

Dilation:

Squish

stretch

$$\left(1,4\right)$$  

$$\left(4,4\right)$$

squish

reflection

6

4

up

2

1

3

5

down

left

right

$$f\left(x\right)=\left(x-3\right)^2+4$$ ; neither even nor odd function

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

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

neither even nor odd function

even function

odd function

Vertical stretch by a factor of 5

Vertical shrink/compress by a factor of 5

Reflect over x-axis

Vertical shift up 5 units

Horizontal shift left 4

Vertical shift up 4

Horizontal shift right 4

Vertical shift down 4

(h,k) = (-3,-2)

(h,k) = (2,-3)

(h,k) = (-2,3)