Horizontal and Vertical Shifts of Quadratic Functions

Describe the transformations of f(x) when compared to the parent function.
f(x)=(x+7)²

• horizontal shift left 7 units

• horizontal shift right 7 units

• vertical shift up 7 units

• vertical shift down 7 units

Which equation describes the transformation of shifting f(x)=x² two units right?

• x² + 2

• x² - 2

• (x + 2)²

• (x - 2)²

Given f(x) = (x-3)² + 5.  What transformations took place from the original function f(x)?

• Left 3 and up 5

• Right 3 and down 5

• Left 3 and down 5

• Right 3 and up 5

Match the equation to its description.

• Right 2 and up 2

• Left 2 and up 2

• Right 2 and down 2

• Left 2 and down 2

Which of these graphs is the same as the parent function y = x² only shifted 8 units right?

• y = (x – 8)²

• y = (x + 8)²

• y = x² + 8

• y = x² – 8

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 graph of the quadratic function q is shown on the grid.

If f(x) = x² and q(x) = f(x) - n, what is the value of n?

Hint: Plug both functions into Desmos!

Just type in the value, NOT "n= ..."

(a)  

Answer explanation

Look where your original vertex was and count how many units DOWN it shifted.

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

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

• left 5

• right 5

• up 5

• down 5

Describe the horizontal shift for y = 3(x + 4)² - 1

• shifts 3 left

• shifts 4 left

• shifts 4 right

• shifts 1 left