The graph of $f ( x ) = ( x - 1 ) ^ { 2 } + 5$ is
A) shifted 1 unit to the right of $y = x ^ { 2 }$ and up 5 units.
B) shifted 1 unit to the left of $y = x ^ { 2 }$ and up 5 units.
C) shifted 1 unit to the right of $y = x ^ { 2 }$ and down 5 units.
D) shifted 1 unit to the left of $y = x ^ { 2 }$ and down 5 units.

Question

Quizplus · Accepted Answer

Looking at the form of the function $f(x)=(x-1)^2+5$, we can see that it is obtained by taking $y=x^2$ and shifting it to the right by 1 unit (by adding $1$ to $x$) and up by 5 units (by adding $5$). Therefore, choice (A) is correct. Choice (B) would be correct if the function were $f(x)=(x+1)^2+5$ instead.

The Graph Of f(x)=(x−1)2+5f ( x ) = ( x - 1 ) ^ { 2 } + 5f(x)=(x−1)2+5

The Graph Of $f ( x ) = ( x - 1 ) ^ { 2 } + 5$