Quadratic Transformations Worksheets

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

• (h,k)

• (3, 1)

• (-1,-3)

• (-1,3)

What does the quadratic function that has a vertex of (3,4) look like?

• y = a(x+3)² + 4

• y = a(x-3)² + 4

• y = -a(x+3) - 4

• y = a(x-3)² - 4

What steps transform the graph y = x² to y = -1/2(x-4)² + 1?

• Compressed by 1/2, shifted 4 units right and 1 unit up

• Reflected across x-axis, compressed by 1/2, shifted 4 units right and 1 unit up

• Reflected across x-axis, stretched by 1/2, shifted 4 units left and 1 unit up

• Stretched by 1/2, shifted 4 units right and 1 unit down

Identify the vertex of f(x) = 5(x+6)² - 7

• (5,6)

• (0,0)

• (6,-7)

• (-6,-7)

What steps transform the graph y = x² to y = x² + 8

• shifted up 8 units

• shifted down 8 units

• shifted left 8 units

• shifted right 8 units

What steps transform the graph y = x² to y = (x - 4)²

• Shifted down 4 units

• Shifted left 4 units

• Shifted right 4 units

• Shifted up 4 units

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

• a reflection across the line x = -4

• a reflection across the line y = -4

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

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

Which list orders the quadratic functions from narrowest to widest?

• y = x² 
  y = 4x² 
  y = 2x² - 2  
  y = 0.5 x²

• y = 0.5 x²  
   y = x² 
  y = 2x² - 2 
  y = 4x²

• y = 4x² 
  y = 2x² - 2
   y = x² 
  y = 0.5 x²  

•  y = 2x² - 2
   y = 4x²
   y = 0.5x²
   y = x²

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

How did we transform from the parent function?
y = x² + 2

• horizontal shift up

• vertical shift up

• horizontal shift down

• vertical shift down