Translations of the Quadratic Function in Vertex Form

Identify the vertex: y = (x+1)² + 4

(-1, 4)

Identify the vertex: y = 0.2(x+4)²

(-4, 0)

Identify the vertex: y = -2x² - 2

(0, -2)

Describe the transformations from the parent function to: y = (x+1)² + 4

Horizontal translation 1 unit to the left and vertical translation 4 units up.

Describe the transformations from the parent function to: y = 1/3(x+2)² - 7

Horizontal translation 2 units to the left and vertical translation 7 units down.

Describe the transformations from the parent function to: y = (x-4)² - 5

Horizontal translation 4 units right, and vertical translation 5 units down.

Describe the transformations from the parent function to: y = 0.2(x+4)²

Horizontal translation 4 units to the left.

Describe the transformations from the parent function to: y = (x-7)² - 3

Horizontal translation 7 units to the right and vertical translation 3 units down.

What does changing the "h" variable do to the graph of a quadratic function?

Horizontally translates the graph (moves the parabola right or left).

Describe the transformations from the parent function to: y = -(x+2)² + 7

Reflection, horizontal translation 2 units to the left and vertical translation 7 units up.

Describe the transformations from the parent function to: y = -(x+3)² - 5

Reflection, horizontal translation 3 units to the left and vertical translation 5 units down.

Describe the transformations from the parent function to: y = -(x-6)² + 9

Reflection, horizontal translation 6 units to the right and vertical translation 9 units up.

Describe the transformations from the parent function to: y = -(x+8)² + 11

Reflection, horizontal translation 8 units to the left and vertical translation 11 units up.

Describe the transformations from the parent function to: y = -2x² - 2

Reflection, vertical translation 2 units down.

What does changing the "k" variable do to the graph of a quadratic function?

Vertically translates the graph (moves the parabola up or down).

Identify a, h, and k: y = -(x+8)² + 11

a = -1, h = -8, k = 11

Identify a, h, and k: y = -4(x-8)² + 11

a = -4, h = 8, k = 11

If, from the parent function, a quadratic has the following transformations, what is the equation of the quadratic function in vertex form? - Horizontal translation 2 units left - Vertical translation 3 units up

y = (x + 2)² + 3

If, from the parent function, a quadratic has the following transformations, what is the equation of the quadratic function in vertex form? - Reflection - Horizontal translation 2 units right - Vertical translation 3 units down

y = -(x - 2)² - 3

If a = -1/2, h = 8, and k = -3 What is the equation of the quadratic function in vertex form?

y = -1/2(x - 8)² - 3

If a = 2, h = -3, and k = 5 What is the equation of the quadratic function in vertex form?

y = 2(x + 3)² + 5

What is the vertex form of a quadratic function?

y = a(x - h)² + k