Vertical and Horizontal Transformation of Quadratic Functions

Name the parent function.

• linear
• quadratic
• cubic
• logarithmic

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.HSF.IF.C.7

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

CCSS.HSF.IF.B.4

CCSS.HSA.CED.A.2

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

• a vertical translation 4 units up
• a vertical translation 4 units down
• a horizontal translation 4 units to the left
• a horizontal translation 4 units to the right

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.C.7

CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.4

• horizontal shift left 12 units

• horizontal shift right 12 units

• vertical shift up 12 units

• vertical shift down 12 units

Tags

CCSS.HSF.BF.B.3

Describe the transformations of f(x) when compared to the parent function.
f(x) = (x+7)²

• horizontal shift left 7 units
• horizontal shift right 7 units
• vertical shift up 7 units
• vertical shift down 7 units

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

If the blue is f(x) = x^2, the red must be

• g(x) = (x+3)²

• g(x) = (x-3)²

• g(x) = x² + 3

• g(x) = x² - 2

Tags

CCSS.HSF.BF.B.3

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

What is the vertical shift of this equation? (look at the end of the equation)
f(x) = -(x + 3)² - 5

• left 5
• right 5
• up 5
• down 5

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.C.7

What is the parent function of a quadratic equation (matches this graph)?

• y = |x|

• y = x

• y = x²

• y = 2^x

Tags

CCSS.HSF.IF.C.7

CCSS.HSA.REI.D.10

CCSS.HSF.IF.B.4

In the graph of the function y=x², which describes a vertical shift in the parent function up 5 units?

• y = x² - 5
• y = x² + 5
• y = (x - 5)²
• y = (x + 5)²

Tags

CCSS.HSF.BF.B.3

• Shift up 2 units

• Shift down 2 units

• Shift right 2 units

• Shift left 2 units

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2