Quadratic Transformations

Verbal Transformations

100

Zack sketches a parabola with a vertex at the origin that opens downward. What is the equation of Zack's function?

y = -x^2

200

Dakota translates the quadratic parent function 10 units to the right and 4 units down. What is the equation of Dakota's function?

y = (x-10)^2 - 4

300

Gloria transforms the quadratic parent function by vertically stretching the parabola by a factor of 2. Then, she translates the parabola 8 units up and 6 units right. What is the equation of Gloria's parabola?

y = 2(x-6)^2 + 8

400

Makayla begins with the quadratic parent function. She reflects the parabola over the x-axis and translates the function 3 units to the left and 5 units down. What is Makayla's equation?

y = -(x+3)^2 - 5

500

A'Shantis transforms a quadratic function by stretching it vertically by a factor of 4 and translating the parabola 22 units down and 1 unit to the left. What is the equation of the transformed function?

y = 4(x+1)^2 - 22

Describing Transformed Equations

100

y = (x+1)^2 - 5

Translated 1 unit left and 5 units down.

200

y = 1/6(x-3)^2 + 1

Vertically compressed, and translated 3 units to the right and 1 unit down.

300

y = -4(x+2)^2 + 4

Reflected across the x-axis, vertically stretched, and translated 2 units to the left and 4 units up.

400

y = -1/3(x)^2

Vertically compressed and reflected across the x-axis.

500

y = 2x^2 + 15

Vertically stretched and translated 15 units up.

Describing Transformed Equations

100

y = 3x^2 - 6

Vertically stretched by a factor of 3 and translated 6 units down.

200

y = 2x^2 + 10

Vertically stretched, and translated 10 units up.

300

y = 6(x+1)^2 + 9

Vertically stretched and translated 1 unit left and 9 units up.

400

y = 5x^2

Vertically stretched

500

y = 2/5x^2

Vertically compressed

Transformations in Function Notation

100

f(x-7)

Translated 7 units right.

200

f(x-3) + 21

Translated 3 units to the right and 21 units up.

300

3f(x)

Vertically stretched.

400

f(2/3x)

Horizontally stretched.

500

-f(x)

Reflected over the x-axis.

Transformations in Function Notation

100

f(x) + 4

Translated 4 units up.

200

2/3f(x)

Vertically compressed.

300

1/5f(x) - 4

Vertically compressed and translated 4 units down.

400

-f(x)

Reflected over the x-axis

500

8f(x-3) - 4

Vertically stretched and translated 3 units to the right and 4 units down.