Graphing and Transforming Quadratic Functions in Vertex Form

Describe the transformations from f(x)=x² to g(x)=1/4x²+4

• Reflected across x axis, up 4 units

• Vertical shrink by 1/4, up 4 units

• Vertical stretch by 4, up 4 units

• Vertical string by 1/4, left 4 units

Which of the following is true when the graph of f(x)=x²+4 is transformed into the graph g(x)=2x²+4

• The new function has more zeroes than the old function

• Both functions have the same vertex

• The function is translated up

• The axis of symmetry changes

Comparing h(x)=-5x²-1 to the parent function f(x)=x², determine which transformation DOES NOT occur.

• Reflection over the x-axis

• Vertical stretch by a factor of 5

• Down 1 unit

• Reflected over the y-axis

Which function's graph is the result of shifting the graph of f(x)=-x²-4 3 units down?

• g(x)=-x²-1

• g(x)=-4x²-4

• g(x) = -1/3x²-4

• g(x)=-x²-7

Tags

CCSS.HSF-IF.C.7A

Which of the following describes the transformations that occurred from y = x² to obtain the graph of y = 2x² + 4?

• narrower by 2 and translation up 4

• wider by 2 and translation up 4

• narrower by 2 and translation left 4

• wider by 2 and translation right 4

If the blue graph is
f(x) = x² 
the red must be...

• g(x) = (x + 3)²

• g(x) = (x - 3)²

• g(x) = x² + 3

• g(x) = x² - 2

Abigail is designing a garden and wants to create a blueprint. If the blue graph represents the area of a square garden as
f(x) = x² 
then the red graph must represent the area of a garden with a different feature. What is the equation for the red graph?

• g(x) = x² - 5

• g(x) = x² + 5

• g(x) = (x - 5)²

• g(x) = (x + 5)²

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

Comparing to f(x)=x², select all of the transformations of g(x)=-5x²+11

• Reflected over x axis

• Vertical stretch by 5

• Vertical stretch by 11

• Up 11

• Left 11