Transformations of Quadratic Functions

Which transformation maps the graph of
f(x) = x² to the graph of g(x) = (x + 4)²?

• a translation shifting f(x) 4 units up

• a translation shifting f(x) 4 units down
• a translation shifting f(x) 4 units to the left
• a translation shifting f(x) 4 units to the right

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.4

CCSS.HSG.CO.A.5

Which transformation will occur if f(x) = x² is replaced with 2⋅f(x)?

• Wider

• Narrower

• Vertical translation up by 2 units.
• Reflection across the x-axis.

Tags

CCSS.HSF.BF.B.3

Which transformation will occur if f(x) = x² is replaced with f(x) + 2?

• Translation left 2 units

• Narrower

• Vertical translation up by 2 units.
• Reflection across the x-axis.

Tags

CCSS.HSF.BF.B.3

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

• (-2, 5)
• (-6, 5)
• (-4, 3)
• (-4, 7)

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.C.7

CCSS.HSF.IF.B.4

f(x) is transformed so that it maps onto g(x). Which equation would correctly represent g(x)

• g(x)=f(x + 3)
• g(x)=f(x - 3)
• g(x)=f(x) + 3
• g(x)=f(x) - 2

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

CCSS.HSF.IF.C.7

The vertex of the quadratic function f(x) = -2x² + 4x + 3 if (1, 5). If g(x) = f(x - 2), what is the vertex of g(x)

• (1, 3)
• (1, 7)
• (-1, 5)
• (3, 5)

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.C.7

How did we transform from the parent function?
g(x) = -1/5(x - 1)² + 7

• reflection, vertical compression, horizontal right, vertical up
• vertical compression, horizontal shift left, vertical shift up
• reflection, horizontal shift right, vertical shift down
• no changes were made to y = x²

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

Which quadratic function is represented by the graph?

• y = 2(x - 4)² + 5
• y = 2(x + 4)² + 5
• y = -2(x - 4)² + 5
• y = -2(x + 4)² + 5

Tags

CCSS.HSF-IF.C.7A

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

Tags

CCSS.HSF.BF.B.3

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

What transformations occurred to get f(x), the red graph, to become g(x), the blue graph?

• horizontal shift down and vertical shift left
• horizontal shift left and vertical shift down
• horizontal shift right and vertical shift up
• horizontal shift up and vertical shift right

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.4

CCSS.HSG.CO.A.5