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

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 $- \frac { 1 } { 81 }$ .

Quizplus · Accepted Answer

The expression $-\frac{1}{9}(x+6)$ indicates a horizontal shift left by 6 units and a vertical shift downward by 1 unit. The factor $-\frac{1}{9}$ inside the square indicates a horizontal stretch by a factor of 9, which results in a vertical shrink by a factor of $\frac{1}{81}$ when squared.

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