Transformations of Parabolas

Given f(x) = (x-3)² + 5.  What transformations took place from the original function f(x)?

• Left 3 and up 5
• Right 3 and down 5
• Left 3 and down 5
• Right 3 and up 5

• Shifted up 5

• Shifted down 5

• Reflection over the x-axis

• Reflection over the y-axis

  The blue function is the original function f(x) = x³.  Which of the following is the correct equation for the red function, g(x)?

• g(x)=x³+1
• g(x)=x³-1
• g(x)=(x-1)³
• g(x)=(x+1)³

• Vertical Stretch

• Vertical Compression

• Translation up 5 units

• Reflection across the x-axis

• horizontal shift left 7 units

• horizontal shift right 7 units

• vertical shift up 7 units

• vertical shift down 7 units

• Vertically stretched by a factor of 2, right 3, and up 1

• Vertically compressed by a factor of 1/2, left 3 and down 1

• Vertically compressed by a factor of 1/2, right 3, and down 1

• Vertically stretched by a factor of 2, left 3, and up 1

• Right 2 and up 2

• Left 2 and up 2

• Right 2 and down 2

• Left 2 and down 2

• Shifted up 5

• Shifted down 5

• Reflection over the x-axis

• Reflection over the y-axis

Which equation describes the transformation of shifting f(x)=x² two units right?

• x² + 2
• x² - 2
• (x + 2)²
• (x - 2)²

• 4 units up

• 4 units to the left

• 4 units to the right

• 4 units down