Transformations

Question

let f(x) = x² 

Determine the values of a, h, and k that produce g(x) which is the function f(x) after a vertical shift down 7 units. 

Answer 1

General equation:

 

g(x) = a(x-h)² + k

• a = vertical dilation
• h = horizontal shift
• k = vertical shift

 

f(x) = 1·(x-0)² + 0 = x²

 

We want a vertical shift of 7 down (-7)

 

g(x) = 1·(x-0)² + (-7) = x² - 7

Answer 2

Y=x^2-7

 

  = 1(x-0)^2 - 7

 

A=1

(H,k)= (0,-7)