Given f ( x ) = x ^2 , after performing the following transformations: shift upward 58 units and shift 21 units to the right, the new function g ( x )

Question

Given
f
(
x
)
=
x
2
f
x
x
2
, after performing the following transformations: shift upward 58 units and shift 21 units to the right, the new function
g
(
x
)

Answer 1

A shift 21 units to the right yields

 

g(x) = (x - 21)²

 

 

A shift 58 units up from this position is

 

g(x)= (x - 21)² + 58

 

 

This transformed function is a parabola with a vertex of (21, 58).  So basically, we moved the vertex from the point (0, 0) to the point (21, 58).