Quadratic Function Dilations

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

How did we transform from y=x^2?

y = -3x²

• vertical reflection and vertical shift down

• vertical reflection and vertical stretch

• horizontal stretch

• vertical reflection and vertical compression

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

Match the description to its equation.
Reflected over the x-axis 
Stretched by a factor of 2

• A

• B

• C

• D

Given f(x) = ax² , if 0 < a < 1 , the graph will transform by

• becoming wider or vertically compressed

• becoming narrower or vertically stretched

Which equation matches the following transformation: up 4, stretched 3, reflected down, and left 1

What is the vertex form of a quadratic function?

• f(x) = 2a(x-h)² + k

• f(x) = a(x-h)² + k

• f(x) = (x+h)² + k

• f(x) = a(x-h) - k

• Vertical compression (wider)

• Vertical stretch (narrower)

• Vertical compression (wider) and reflection over x-axis

• Vertical stretch (narrower) and reflection over x-axis

Let the graph of g be a translation 2 units down and 4 units left of the graph of f(x) = x². Write a rule for g.

• g(x) = (x - 4)² - 2

• g(x) = (x + 4)² - 2

• g(x) = (x - 4)² + 2

• g(x) = (x + 4)² + 2

Identify the function graphed here.