Quadratic Functions Transformations With Pictures

Does the graph of this equation open up or down?

f(x) = -(x + 3)² - 5

• up

• down

Tags

CCSS.HSF-IF.C.7A

A parabola has a vertex at (-3,2).
Where is the axis of symmetry?

• y = -2

• x = 3

• x = -3

• y = 2

What transformations occurred to get f(x), the red graph, to become g(x), the blue graph?

• horizontal shift down and vertical shift left

• horizontal shift left and vertical shift down

• horizontal shift right and vertical shift up

• horizontal shift up and vertical shift right

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 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

How did we transform from f(x) =x² 
to
g(x) = -3x²

• reflection in x-axis and vertical shift down

• reflection x-axis and vertical stretch

• horizontal stretch

• reflection x-axis and vertical compression

How did we transform from the parent function?
g(x) = -1/5(x - 1)² + 7

• reflection, vertical compression, horizontal right, vertical up

• vertical compression, horizontal shift left, vertical shift up

• reflection, horizontal shift right, vertical shift down

• no changes were made to y = x²

Match the description to its equation:
moves down 3

• A

• B

• C

• D

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

What is the vertical shift of this equation?
f(x) = -(x + 3)² - 5

• left 5

• right 5

• up 5

• down 5