Compare the graph of $p ( x ) = \left[ - \frac { 1 } { 3 } ( x + 9 ) \right] ^ { 2 } - 9$ with $p ( x ) = x ^ { 2 }$.
A) $p ( x ) = \left[ - \frac { 1 } { 3 } ( x + 9 ) \right] ^ { 2 } - 9$ shifts right 9 units, shifts downward 9 units, and shrinks by a factor of $- \frac { 1 } { 9 }$.
B) $p ( x ) = \left[ - \frac { 1 } { 3 } ( x + 9 ) \right] ^ { 2 } - 9$ shifts right 81 units, shifts upward 9 units, and shrinks by a factor of $\frac { 1 } { 9 }$.
$p ( x ) = \left[ - \frac { 1 } { 3 } ( x + 9 ) \right] ^ { 2 } - 9$ shifts left 9 units, shifts downward 9 units, and shrinks
C) by a factor of $\frac { 1 } { 9 }$.
$p ( x ) = \left[ - \frac { 1 } { 3 } ( x + 9 ) \right] ^ { 2 } - 9$ shifts right 9 units, shifts upward 9 units, and shrinks by
D) a factor of $\frac { 1 } { 9 }$. $p ( x ) = \left[ - \frac { 1 } { 3 } ( x + 9 ) \right] ^ { 2 } - 9$ shifts left 81 units, shifts upward 9 units, and shrinks by
E) a factor of $- \frac { 1 } { 3 }$.

Question

Quizplus · Accepted Answer

The correct transformation involves a leftward shift of 9 units (due to $x+9$), a downward shift of 9 units (due to $-9$ at the end), and a vertical shrink by a factor of $\frac{1}{9}$ (since the coefficient $-\frac{1}{3}$ squared gives $\frac{1}{9}$).

Compare the Graph Of p(x)=[−13(x+9)]2−9p ( x ) = \left[ - \frac { 1 } { 3 } ( x + 9 ) \right] ^ { 2 } - 9p(x)=[−31​(x+9)]2−9

Compare the Graph Of $p ( x ) = \left[ - \frac { 1 } { 3 } ( x + 9 ) \right] ^ { 2 } - 9$