Identifying Transformation of Quadratic Function 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

Abigail is designing a garden and wants to create a blueprint. If the blue graph represents the area of a square garden as
f(x) = x² 
then the red graph must represent the area of a garden with a different feature. What is the equation for the red graph?

• g(x) = x² - 5

• g(x) = x² + 5

• g(x) = (x - 5)²

• g(x) = (x + 5)²

Given f(x) = (x + 6)² - 2 , how did we transform from the parent function?

• Horizontal shift left 6, vertical shift up 2

• Horizontal shift left 6, vertical shift down 2

• Horizontal shift right 6, vertical shift down 2

• Horizontal shift right 6, vertical shift up 2

Which of the following describes the transformations that occurred from y = x² to obtain the graph of y = 2x² + 4?

• narrower by 2 and translation up 4

• wider by 2 and translation up 4

• narrower by 2 and translation left 4

• wider by 2 and translation right 4

• Shifted 2 units to the right and 3 units up

• Shifted 2 units to the left and 3 units down

• Shifted 2 units to the right and 3 units down

• Shifted 2 units to the left and 3 units up

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)

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