Algebra 1- Quadratic Transformations

Verbal Transformations- Part 1

100

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

y = -x^2

200

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

y = (x-10)^2 - 4

300

Tenley 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 Tenley's parabola?

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

400

Liv 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 Liv's equation?

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

500

Aiden 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

Describe Transformed Equations- Part 1

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 = 2x² + 15

Streched by a scale factor of 2 and translated 15 units up.

Describe Transformed Equations- Part 2

100

y = 3x² - 6

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

200

y = 2x² + 10

Vertically stretched by a factor of 2, and translated 10 units up.

300

y = 6(x+1)² + 9

Stretched by a factor of 6, translated 1 unit left and 9 units up.

400

y = 5x²

Vertically stretched by a factor of 5

500

y = -(2/5)(x+7)² - 4

Reflection over the x-axis, compression by 2/3, left 7, and down 4

Describe Transformed Equations-Part 3

100

y = (x-7)^2

Translated 7 units right.

200

y = (x-3)^2 + 21

Translated 3 units to the right and 21 units up.

300

y = 3x²

Vertically stretched by a factor of 3

400

y = (2/3)x²

Compression by a factor of 2/3

500

y = -2(x+3)² + 4

Reflected over x-axis, vertically stretched by a factor of 2, left 3, and up 4

Verbal Transformations- Part 2

100

f(x) + 4

Translated 4 units up.

200

2/3f(x)

Vertically compressed.

300

f(1/5x) - 4

Horizontally stretched and translated 4 units down.

400

f(-x)

Reflected over the y-axis

500

8f(x-3) - 4

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