Parabola Translations

It is the vertex

It is an x-intercept

It is the y-intercept

It is the axis of symmetry

Stretch

Shrink

y = 2x² + 1

y = 7x² - 1

y = 0.5x² + 1

y = x²

y = 0.5x² + 2

y = x²

y = 10x² + 7

y = - 3x² - 2

Stretch/Non-reflection

Shrink/Non-reflection

Stretch/Reflection

Shrink/Reflection

Reflection

Non-reflection

Reflection

Non-reflection

Vertical translation 7 units down

Vertical translation 7 units up

Horizontal translation 7 units left

Horizontal translation 7 units right

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

Shifted down 4 units

Shifted left 4 units

Shifted right 4 units

Shifted up 4 units

Horizontal shift left 3

Vertical shift up 3

Horizontal shift right 3

Vertical shift down 3

(-4 , 1)

(-4 , -1)

(4 , -1)

(4 , 1)

Vertically translated 2 units down and horizontally translated 4 units right

Vertically translated 4 units down and horizontally translated 2 units left

Vertically translated 2 units down and horizontally translated 4 units left

Vertically translated 4 units up and horizontally translated 2 units right

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

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

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

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

$$y=\left(x-2\right)^2$$

$$y=\left(x+2\right)^2$$

$$y=x^2-2$$

$$y=x^2+2$$