Write an equation for the function that is described by the given characteristic.
The shape of $f ( x ) = x ^ { 2 }$ ,but shifted three units to the right and five units downward.

A) $g ( x ) = ( x - 3 ) ^ { 2 } - 5$
B) $g ( x ) = \left( x ^ { 2 } - 3 \right) - 5$
C) $g ( x ) = ( x + 3 ) ^ { 2 } - 5$
D) $g ( x ) = ( x + 3 ) ^ { 2 } + 5$
E) $g ( x ) = ( x - 3 ) ^ { 2 } + 5$

Question

Write an equation for the function that is described by the given characteristic. ​
The shape of $f ( x ) = x ^ { 2 }$ ,but shifted three units to the right and five units downward.
​
A) $g ( x ) = ( x - 3 ) ^ { 2 } - 5$
B) $g ( x ) = \left( x ^ { 2 } - 3 \right) - 5$
C) $g ( x ) = ( x + 3 ) ^ { 2 } - 5$
D) $g ( x ) = ( x + 3 ) ^ { 2 } + 5$
E) $g ( x ) = ( x - 3 ) ^ { 2 } + 5$

Quizplus · Accepted Answer

Shifting the graph of $f(x) = x^2$ three units to the right is achieved by replacing $x$ with $x-3$, resulting in $(x-3)^2$. Shifting five units downward is achieved by subtracting 5, leading to the equation $g(x) = (x-3)^2 - 5$.

Write an Equation for the Function That Is Described by the Given