Transformations of Quadratic Functions

Which transformation moves the graph of

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

• a translation 4 units up

• a translation 4 units down

• a translation 4 units to the left

• a translation 4 units to the right

Tags

CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.4

CCSS.HSG.CO.A.5

If the blue is f(x) = x^2, 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.IF.C.7

CCSS.HSF.IF.B.4

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

CCSS.HSA.SSE.B.3

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

 (Blue is f(x) and red is g(x) )

• $g\left(x\right)\ =\ 2x^2$
  

• $g\left(x\right)\ =\ 0.5x^2$

• $g\left(x\right)\ =\ x^2\ +\ 2$
  

• $g\left(x\right)\ =\ \left(x+2\right)^2$
  

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.C.7

If blue is f(x), and red is g(x), which equation would correctly represent g(x)?

• $g\left(x\right)\ =\ \left(x+3\right)^2$

• $g\left(x\right)\ =\ \left(x-3\right)^2$
  

• $g\left(x\right)\ =\ x^2+3$
  

• $g\left(x\right)\ =\ x^2-3$
  

Tags

CCSS.HSF.IF.C.7

CCSS.HSF.IF.B.4

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

CCSS.HSA.SSE.A.1

How do you transform from f(x) = x² to g(x) = -3x² ?

• move down 3

• reflection and vertical stretch by 3

• horizontal stretch by 3

• reflection vertical compression by 3

Tags

CCSS.HSF.BF.B.3

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

In the equation f(x) = 5(x+3)² - 10 what does the 5 do?

• Vertical stretch by 5

• Vertical compress by 5

• Reflect

• Move up 5

Tags

CCSS.HSF.BF.B.3

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

What transformations have occurred? 

• Right 2 and up 2
• Left 2 and up 2
• Right 2 and down 2
• Left 2 and down 2

Tags

CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.4

CCSS.HSG.CO.A.5

CCSS.HSG.CO.B.6

How do you transform from the parent function f(x) = x² to g(x) = -1/5(x - 1)² + 7 ?

• reflection, vertical compression, 1 right, 7 up

• vertical compression, 1 left, 7 up

• reflection, 1 right, 7 up

• reflection, vertical stretch, 1 right, 7 up