Describing Transformations of Quadratic Equations

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

Which describes the transformation of the graph of f(x) = x²  to the graph of  g(x) = -4x²

• Reflected, narrower

• reflected, wider

• shifted down 4 units

• shifted up 4 units

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

• shift 4 units up

• shift 4 units down

• shift 4 units to the left

• shift 4 units to the right

How did we transform from y=x² to

y = -3x²

• reflection in x-axis and shifts down

• reflection x-axis and narrower

• wider

• reflection x-axis and wider

Describe the transformation from the parent graph

• Reflect over x, right 3, down 4

• Reflect over y, right 3, down 4

• Reflect over x, right 3, up 4

• Reflect over y, left 3, down 4

The graph of a quadratic function f is shown and the vertex is labeled with its coordinates.  If g(x) = f(x - 1) + 2, what is the minimum value of g?

* The minimum value of g is ​ (a)   because the minimum value of f is ​ (b)   and the graph of g is shifted ​ (c)   from the graph of f by ​ ​ (d)   .​

• 6

• 4

• up

• 2

• 1

• 3

• 5

• down

• left

• right

The graph of a transformed squaring function is shown below. Which equation and description best describes the graph? Select the equation ​ (a)   and description ​ (b)  

• neither even nor odd function

• even function

• odd function

Describe the transformations from the original parent function f(x) = x².

g(x) = 5x² + 2

• Vertical Stretch of 5

  Vertical Down 2

• Vertical Compression of 5

  Vertical Up 2

• Vertical Stretch of 5

  Vertical Up 2

• Vertical Compression of 5

  Vertical Down 2

• (h,k) = (2,-3)

• 
• (h,k) = (-3,-2)

• 
• (h,k) = (-2,3)

• 

The graph of a transformed squaring function is shown below. Which equation and description best describes the graph? Select the equation ​ (a)   and description ​ (b)  

• neither even nor odd function

• even function

• odd function