Shift the graph of $f ( x ) = x ^ { 2 }$ by $6$ units to the left and then $4$ units downward, and choose the equation for the final transformed graph.
A) $f ( x ) = \left( x ^ { 2 } + 6 \right) - 4$
B) $f ( x ) = ( x + 6 ) ^ { 2 } - 4$
C) $f ( x ) = ( x + 4 ) ^ { 2 } + 6$
D) $f ( x ) = ( x - 6 ) ^ { 2 } - 4$
E) $f ( x ) = ( x - 4 ) ^ { 2 } + 6$

Question

Quizplus · Accepted Answer

To shift the graph of $f(x) = x^2$ by 6 units to the left, replace $x$ with $x + 6$, resulting in $(x + 6)^2$. To then shift it 4 units downward, subtract 4 from the result, leading to the equation $f(x) = (x + 6)^2 - 4$.

Shift the Graph Of f(x)=x2f ( x ) = x ^ { 2 }f(x)=x2

Shift the Graph Of $f ( x ) = x ^ { 2 }$