Identifying Transformations in Vertex Form

What is the translation from the green graph to the orange graph?

• Right 6, up 2

• Right 6, down 2

• Left 6, down 2

• Left 6, up 2

What is the translation from the red graph to the blue graph?

• Right 3, down 4

• Left 3, down 4

• Right 3, up 4

• Left 3, up 4

What is the translation from the purple graph to the black graph?

• Left 2, down 7

• Right 2, down 7

• Up 7

• Down 7

What is the translation from f(x) to g(x)?

• Left 4, down 9

• Left 4, up 9

• Right 4, down 9

• Left 10, up 9

If the blue graph is
f(x) = x² 
then the red must be...

• g(x) = x² - 5

• g(x) = x² + 5

• g(x) = (x - 5)²

• g(x) = (x + 5)²

Write the equation of a parabola that has shifted 4 units to the right, 5 units down, and has flipped over the x-axis. (a)  

• y = - (x - 5)2 + 4

• y = - (x - 4)2 - 5

• y = - (x + 4)2 - 5

• y = - (x + 5)2 + 4

Describe the transformations of y = -0.5(x + 3)² ?

• shift right 3, reflect, and wide

• shift up 3, reflect, and wide

• shift left 3, reflect, and wide

• shift down 3, reflect, and wide

Given f(x) = (x + 3)² , how did we transform from the parent function?

• Horizontal shift left 3

• Vertical shift up 3

• Horizontal shift right 3

• Vertical shift down 3

The vertex of the quadratic function f(x) in the picture is (-4, 5). If g(x) = -f(x - 2) - 3 , what is the vertex of g(x)?

• (-6, -8)

• (-2, 2)

• (-2, -2)

• (-2, -8)

• Shifted 2 units to the right and 1 unit up

• Shifted 2 units to the left and 1 unit down

• Stretched by a factor of 3 and shifted 2 units to the right

• Stretched by a factor of 3, shifted 2 units to the right, and 1 unit up