Transformations of Vertex Form

Which function has a translation of 2 units right and a vertical stretch by a factor of 5?

• f(x)= 5(x - 2)²

• f(x) = 5(x + 2)²

• f(x) = (x - 2)² - 5

• f(x) = (x + 2)² + 5

What is the vertex form of a quadratic function?

• f(x) = 2a(x-h)² + k

• f(x) = a(x-h)² + k

• f(x) = (x+h)² + k

• f(x) = a(x-h) - k

What is the axis of symmetry in the function f(x) = (x-1)² +2

• x = 1

• x = -1

• x = 2

• x = -2

Identify the vertex of f(x) = -2(x+1)² + 3

• (h,k)

• (3, 1)

• (-1,-3)

• (-1,3)

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)

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

• g(x) = (x + 3)²

• g(x) = (x - 3)²

• g(x) = x² + 3

• g(x) = x² - 2

• 3

• -9

• 0

• -3

• 9

• -2

• -6

• 2

• 6

• 0

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

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