Transformations of Quadratic Functions

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

Match the description to its equation.
Stretches by a factor of 3

• A

• B

• C

• D

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

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

The parent function, f(x), is transformed so that it maps into g(x). Which equation would correctly represent g(x)?

(a)  

• g(x)=f(x - 3)

• g(x)=f(x + 3)

• g(x)=f(x) + 3

• g(x)=f(x) - 2

"a" causes the parabola to vertically ​ (a)   when a > 1.

• stretch

• compress

a

b

c

d

e

left

down

right

up

reflected

Label how each number transforms the function

b

c

d

e

Reflected over the x-axis

Left 3

Moves up 7

Right 3

Stretched by a factor of 2

a

b

c

d

Horizontal Translation

Vertical Translation

Vertical Dilation

Horizontal Dilation

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