Transformations Quadratic Graphs

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

The equation of red graph is y = x². What is the equation of the blue graph?

• y = (x + 2)² + 3

• y = 3(x + 2)²

• y = (x - 2)² + 3

• y = (x + 2)² - 3

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

• a vertical shift 4 units up

• a vertical shift 4 units down

• a horizontal shift 4 units to the left

• a horizontal shift 4 units to the right

How did we transform from the parent function?

• reflection, vertical compression, horizontal shift right, vertical shift up

• vertical compression, horizontal shift left, vertical shift up

• reflection, horizontal shift right, vertical shift down

• no changes were made to y = x²

If red represents y = x², which equation represents blue?

• y = 2x²

• y = -2x²

• y = -x²

• y = (x - 1)²

Tags

A1.FBF.3

If the blue graph is f(x), the red must be...

• g(x) = f(x + 3)

• g(x) = f(x - 3)

• g(x) = f(x) + 3

• g(x) = f(x) - 2

• Reflection over x-axis

• None of these

The graph of the function f(x) = x² was transformed to form the graph of g(x) = (x – 7)² + 8. Which transformations occurred to create the graph of g?

• A shift of 7 units to the right and 8 units up.

• A shift of 7 units to the left and 8 units up.

• A shift of 7 units to the right and 8 units down.

• A shift of 7 units to the left and 8 units down.

Answer explanation

Tool: Calculator Graph & Describe movement/transformations.

If the function f(x) = x² is changed so that a new function is created, g(x) = 5x², how does g(x) compare to f(x)?

• The graph of g(x) is wider than the graph of f(x)

• The graph of g(x) is narrower than the graph of f(x)

• The graph of g(x) is shifted 5 units up above f(x)

• The graph of g(x) is shifted 5 units down below f(x)

Tags

A1.FBF.3

The graph shows the function f(x)=x² in blue and another function g(x) in red.  Which could be the equation for g(x)?

• g(x) = 2x²

• g(x) = 1/2x²

• g(x) = x² + 2

• g(x) = (x + 2)²