Compare the graph of $n = \left[ - \frac { 1 } { 9 } ( x + 6 ) \right] ^ { 2 } - 1$ with $n ( x ) = x ^ { 2 }$ .
A) $n = \left[ - \frac { 1 } { 9 } ( x + 6 ) \right] ^ { 2 } - 1$ shifts left 6 units,shifts downward 1 units,and shrinks by a factor of $\frac { 1 } { 81 }$ .
B) $n = \left[ - \frac { 1 } { 9 } ( x + 6 ) \right] ^ { 2 } - 1$ shifts right 6 units,shifts upward 1 units,and shrinks by a factor of $\frac { 1 } { 81 }$ .?
C) $n = \left[ - \frac { 1 } { 9 } ( x + 6 ) \right] ^ { 2 } - 1$ shifts left 36 units,shifts upward 1 units,and shrinks by a factor of $- \frac { 1 } { 9 }$ .
D) $n = \left[ - \frac { 1 } { 9 } ( x + 6 ) \right] ^ { 2 } - 1$ shifts right 36 units,shifts upward 1 units,and shrinks by a factor of $\frac { 1 } { 81 }$ .
E) $n = \left[ - \frac { 1 } { 9 } ( x + 6 ) \right] ^ { 2 } - 1$ shifts right 6 units,shifts downward 1 units,and shrinks by a factor of $- \frac { 1 } { 81 }$ .

Question

Quizplus · Accepted Answer

The correct transformation of the graph $n = \left[ - \frac { 1 } { 9 } ( x + 6 ) \right] ^ { 2 } - 1$ compared to $n(x) = x^2$ involves a shift to the right by 6 units (due to $x + 6$), a downward shift by 1 unit (due to $-1$), and a vertical shrink by a factor of $\frac{1}{81}$ (since squaring the $-\frac{1}{9}$ results in $\frac{1}{81}$, affecting the vertical stretch/shrink of the graph).

Compare the Graph Of n=[−19(x+6)]2−1n = \left[ - \frac { 1 } { 9 } ( x + 6 ) \right] ^ { 2 } - 1n=[−91​(x+6)]2−1

Compare the Graph Of $n = \left[ - \frac { 1 } { 9 } ( x + 6 ) \right] ^ { 2 } - 1$