Transformations of Functions Quadratic

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

Mathematical Equivalence

ON

The graph of quadratic parent function f was transformed to create the graph of e(x). Which two equations represent the translation on the graph? (Place the f(x) version in the second spot).

Tags

AI.9.6

• up 3

• down 3

• right 1

• left 1

• across x axis

• upward

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)=3x²

• g(x)=1/3x²

• g(x) = x² - 3

• g(x) = (x-3)²

Move the correct answer to each box. Not all answers will be used. ( (a)   , ​ (b)   )

• 3

• -9

• -3

• 0

• 9

Tags

AI.9.7.C

Write the equation of the quadratic function. (parabola)

• y = x² - 1

• y = x² + 1

• y = ( x - 1 )²

• y = ( x + 1 )²

What transformations have occurred? 

• Right 2 and up 2

• Left 2 and up 2

• Right 2 and down 2

• Left 2 and down 2

Which of the following describes the transformations done to the quadratic parent function of f(x) = x² to obtain g(x) = 2x² + 4 ?

• Vertical Stretch by a factor of 2 and vertical shift up 4 units

• Vertical Compress by a factor 2 and vertical shift up 4

• Vertical Stretch by a factor of 2 and horizontal shift left 4 units

• Vertical Compress by a factor of 2 and horizontal shift right 4 units

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

• a vertical translation 4 units up

• a vertical translation 4 units down

• a horizontal translation 4 units to the left

• a horizontal translation 4 units to the right

In the equation f(x)=5(x+3)²-10 what does the 5 do?

• Vertical stretch by 5

• Horizontal compress by 5

• Reflect

• Move up 5